That's an interesting discussion and an intriguing find.
Gleam is important to the history of the Herreshoff Manufacturing Company, because she the very first boat to utilize the unique HMCo building method of building and planking upside down with one mold used per frame.
After having cleaned up at the races in Narragansett Bay she was shipped to England where she arrived with lots of fanfare but did not win many races.
I have never heard that she was shipped back to the U.S. and thus would be surprised if the CBA Gleam and the 1877 Herreshoff Gleam were one and the same vessel. It's a very intriguing thought, though...
Here is what N. G. Herreshoff himself wrote about Gleam:
"August 31 1935
Dear Mr. Stephens -
... There is another amusing thing that occurred while I was at Corliss's; Benjamin Davis of Providence built for Harvey Flint, also of Providence and a most worthy young man, a 25 ft. cat-boat that was very fast and in 1875 and 1876 was winning every race about the Bay. It got to be given out in boating circles, 'The Bristol boats were no longer in first place and Providence had it.' Being in Providence, I heard this remark too often. There were a couple of bright young men of Providence who were much interested in boat sailing George & Frederick Gower. In the fall of 1876 I made an agreement with them that I would build a 25 ft. Cat-boat and they were to take her after she had won in the first general regatta of the Providence Yacht Club in 1877 or had won 2 out of 3 match races with WANDERER of Harvey Flint. I designed and John built for me the GLEAM, and, incidentally, this was the first craft to be built on the system I had worked out - of making a complete mould for each timber over which they were steam-bent and floor timbers attached. The upper end of each mould carried up to a base-line and knee-clips attached to secure to a leveled up floor and bottom up and after bevel fairing the planking is screwed on -thus having the form very exact to design; which is far from the case in the ordinary method. This method has been used by the H.M.Co for all craft under about 75 ft. x 15 ft. o.a., nearly 59 years. The N.Y.Y.C. 50 footers were planked bottom up. This system was expensive for unit construction but it was carried out.
The first meeting of GLEAM with WANDERER was the early general Regatta of the Providence Yacht Club. There was great excitement in yachting circles and there was a large gathering of people & boats at Rocky Point to see the contests. The day was with very fresh southerly wind & light rain, course windward & leeward fully 15 miles. GLEAM beat WANDERER 8 min. and WANDERER was 8 min. ahead of the next boat, so Gowers became owners. Later, the Providence Y.C. held another Regatta over same course in a fine clear day S.S.W. mod. breeze and the Gowers asked me to sail GLEAM. The result was same - 8 min. and WANDERER 9 or 10 min. ahead of the next. Fred Gower later became interested in telephones with Bell & others, and went to England, and had GLEAM shipped there - where he lost his life in ballooning, and it is very interesting that GLEAM became property of Geo. A. Cormack later and now Secretary of New York Yacht Club but then a young man in England. ...
Very truly yours,
Nathanael Greene Herreshoff
Sept. 15 1935."
(Source: Letter 13. From N. G. Herreshoff to W. P. Stephens, dated August 31, 1935 to September 15, 1935. In: Herreshoff, Nathanael Greene and William Picard Stephens. "Their Last Letters 1930-1938." Annotated by John W. Streeter. Bristol, R. I., ca. 1999, p. 67-80.)