"Longboats" meant the largest of several boats available on a ship in Colonial Pre-Revolutionary War Rhode Island.  

William Falconer, An Universal Dictionary of the Marine (London 1789) defines types of boats as the terms were used in the 18th Century, and defines a "longboat" as: the largest boat that usually accompanies a ship, and is generally furnished with a mast and sails, and further describes the longboat as what is common to a merchant-ship.  

Likewise, the U.S. Tables of Allowances for the outfitting of our Naval ships at the beginning of the 19th Century, providing for various boats for the ships, are instructive.  The sloops and brigantines normally had boats over 30 feet in length. See Vol. 31, Nautical Research Journal, p 47 et seq.  (Nautical Research Guild, Bethesda, MD 1985).   There were plenty of sloops and a number of the larger brigantines in the Providence fleet. Again , this suggests that Bowen's "largest long-boats" were easily in excess of 20 feet long.

A wide boat means a long boat.

Bowen's account suggests that the his seat was wide enough for another person to be in the middle (not rowing). 

"I took my seat on the main thwart, near the larboard [left hand side if facing forward in a boat] row-lock, with my gun by my right side, facing forwards. As soon as Dudingston began to hail, Joseph Bucklin, who was standing on the main thwart by my right side,...." 

The persons rowing necessarily cannot be tight against the outside of the boat if there is to be any effective rowing.  A rower needs a two to three foot width of room to row. Two rowers with enough room for a third man to stand on the rowing thwart yields a width of 7 feet or so.  

The existing drawings of longboats of the era  indicate a rather uniform ratio of length, breath, and depth.  This is not surprising, since the colony's and the English shipbuilders knew enough to build on experience and had a body of experience on which to build.  Assuming even a 7 foot width, from Bowen's description of where Joseph Bucklin was standing, and assuming 18th Century standard length to breath dimensions, would yield a longboat length in excess of 18 feet.  Again , this suggests that Bowen's "largest long-boats" were easily in excess of 20 feet long

Large boats were available.

What was the group of ships from which Brown could requisition eight longboats?  By 1772,  the Browns of Providence were engaged in slave trading in Africa and whale hunting in the Atlantic Ocean.  Ships used in both of these enterprises needed more than a small row boat.  For the trading, it was common to anchor relatively far off a shallow shore without a harbor and send the boats back and forth to transport the goods.  For whale hunting, a substantial boat was needed to quickly reach and harpoon and tow the whales. If John Brown really asked for the largest longboats available to him in the harbor, one would not expect a 15 foot rowboat with only 5 single oars to be furnished to him.  

By 1750 shipbuilding in Rhode Island had reached the levels of sophistication of England.  There were common formulas used to determine various aspects of the ship once the length of the ship was agreed upon between purchaser and builder.  Among other common formulas of the day, the length of the ship's "longboat" (largest boat carried on the ship) was figured by taking the square root of the length of the ship and multiplying that square root number by 2.6.   This was found to give a boat capable of being used as a lifeboat in times of disaster far from land, while still being able to be carried on the deck and used without undue difficulty for the many tasks needed by a ship on a long merchant voyage.  If, for example, John Brown's sloop Katy (built 1768) and 110 feet long was equipped in such a way, the "longboat" of the Katy would have been 27 feet long.   Thus, Bowen's description of "largest long-boats" would have meant, to the persons he was addressing, boats of  more than 25 feet long.

Big boats were needed. Also, consider the purpose of the requisition of  the boats.  Brown knew that the attacking force would have to row at least 6 miles, against the tide, and that the final approach might need speed.  For or five  men rowing an overloaded boat would not be what a sailor (and these men were sailors) would use for such an expedition.  Desirable boats for the expedition would be capable of using a minimum of 8 or 10 men rowing.  In short, the longboats used in the Gaspee attack were the largest boats carried on Brown's merchant ships

The boats both available and desirable to Brown would have been capable of large carrying capacity and would have been able to use at least 10 men rowing and 1 man steering without difficulty.  This suggests that Bowen's "largest long-boats" were easily in excess of 25 feet long

Descriptions of the boats other than Bowen's description . What were the descriptions of the boats from others than Bowen?  The attacking force clearly impressed the Gaspee officers and men as being overwhelming is size.  Their estimates were well over a 100 attackers. (E.g., Dickinson said that in the three boats that initially boarded there were 30 or 40 men, and there were a total of 150 that eventually boarded. (The Gaspee's sentinel, Bartholomew Cheever, estimated "about 200.")  Granted that the testimony at the court martial would have emphasized the need to surrender to a superior force.  But the fact is that on the night in question, the English felt overwhelmed, and these are the only estimates of the size of the attacking force. For such a large force, large long-boats were needed.  Again , this suggests that Bowen's "largest long-boats" were easily in excess of 20 feet long, probably closer to 30 feet long.
"I was then sitting with Capt. Tillinghast in the stern of the barge."

John Mawney referred to the long-boat on which he rode as a "barge".  "Barge" was used for two types of boats associated with larger ocean going ships.  An admiral or other high ranking naval officer has on his flagship a "barge".  The barge was a large and imposing boat, and was used to carry the ranking officer to/from his command ship. An admiral's barge, on a first rate ship of the line (100 guns and multiple decks) would have been 40 or so feet long.  It is not the flat bottomed scow that we think of in the 21st Century.  The other 18th Century meaning of "barge" was for the large type of long-boat used to carry goods to and from a ship at anchor and the shore.  Both meanings of the "barge" term used by Mawney indicate a large vessel.  

A large vessel is consistent with his story of first sitting in the stern with the boat captain and then still being able to "spring forward" the length of the boat to be the first in his boat to grab a rope and get aboard the Gaspee.  Obviously, Mawney had room to move between rowers to get forward, so this was not a small boat. that Dickinson said they needed only two boats to take the 19 English sailors and three officers of the Gaspee, as bound captives, and row them ashore. "We were then sent ashore, in two different boats, the Lieutenant and part of the men in one boat, and myself with the rest of the people in the other boat". [Deposition testimony of Dickinson.]   Whether they sat or laid, 22 men bound, in addition to the rowers and others need to maintain the capture of the English sailors, needed a lot of space.
"I had an opportunity of observing the boat, which appeared to me to be a very large long-boat."

Dudingston described one of the attacker's boats thus: 

"During the time they were rowing me on shore, I had an opportunity of observing the boat, which appeared to me to be a very large long-boat. I saw by the man who steered her a cutlass lying by him . . . .One man, who had a little more humanity than any of the rest, said they had better land me at the Point of Pawtuxet. As I was unable to stand, they unbound five of the men and gave them a blanket to carry me up.."  

This description was an attempt by Dudingston to help the investigator discover the attackers' identity, and he was apparently trying to be accurate.  Dudingston was experienced in the English navy, which regularly had longboats in excess of 25 feet long on even their smaller ships.  Dudingston did not describe the boat as a pinnacle, a yawl, or any other kind of smaller rowed boat which were 15 or less feet in length.. He called it a "long-boat," and did not rest on calling it a long-boat or a large long-boat. His description of "a very large long-boat" suggests that Bowen's "largest long-boats" were easily in excess of 25 feet long.  

Likewise, note that there were more than six English men (inferred from Dudingston  saying "they unbound five of the men" ) laying bound and being rowed by the attackers, and (Briggs description) Dudingston laying in the boat behind the space for all the rowers. So for such a cargo of bound or injured men, this boat must have been substantial in size.  In short, Dudingston's description indicates a boat much  longer than 20 feet and more than 4 single oars rowing.

Dickinson testified that he counted seven "launches and merchants ships boats" with "about one hundred and fifty" men.   (Note, Dickinson uses "launch". A "launch" was a sloop- rigged large boat , used by English warships in landing marines for amphibious warfare, a tactic King George favored. The "launch" and the "barge" were the biggest of the ship's boats carried by English warships.) Dickinson clearly wanted to tell the investigators that these 7 boats, with 150 men in them, were large long-boats, easily able to handle 20 plus men in each boat. 

Dudingston and Dickinson were taken ashore in different boats. Dudingston described the boat in such a manner that we can assume it easily accommodate 20 men. Dudingston was probably in Potter's boat, because the description of English sailor Patrick Earle and of Briggs agree regarding  the transport of the captain Dudingston, and because Briggs reported using his small rowboat immediately after the captain was landed. (Brigg's rowboat had been attached to, and towed by, Potter's boat after Briggs  was impressed onto Potter's boat.)

Potter's boat was described by Briggs as: "....he was in a boat which was rowing with eight oars; that the time he met the said Potter was about half an hour after he, this deponent, left the island, and he, said Potter, was about five miles from Bristol; that there were eleven men in said boat."  Briggs was impressed by the Potter group to row.  Whether Briggs was to use an additional available oar or was to give relief to the rowers,  the fact is that Potter's boat had at least four sets of oars, maybe more, was probably in excess of  28 feet, and was fully able to hold 20 men. 

If Potter had a 28 foot long-boat, did Brown?  Brown had a sizeable fleet of merchant ships engaged in the slave and sugar trades, and Providence was a town with a number of ships available in the harbor. Fifty whaling ships made Rhode Island their home base, bringing back spermaceti, the raw materials for Brown's candle making factory.  It is doubtful that Brown in Providence had only smaller long-boats than available to Potter in Bristol. (E.g., see earlier note on this page about the Katy and the probable size of its longboat.)

Whaling was a New England industry, and, as noted above, the Browns had whaling ships available.  The whaleboat that was launched from the whaling ship was a rather standard boat.  The standard whaleboat was about 28 feet long and six feet wide. Whillits D. Ansel, The Whaleboat (Mystic Seaport Museum, 1978).

So, our conclusion, from several independent points,  is that Bowen's description of  "largest long-boats in the harbor" tells us of boats in excess of 25 feet in length, most probably about 30 feet long, and designed to be rowed by 10 men (five pairs of oars).

Consider how many men were involved in the attack on the Gaspee.