The 1774 census of Rhode Island seems only to show three Kimbell families, all in Gloucester, R.I. Only John and Asa showed young males, John with 1 and Asa with 4.
In the 1782 census, there was Asa with 4 and John with 3.
There were also Kimballs, but I’d start with these two men. Have you investigated them? Asa was way up in Barton, Vermont in 1791, so maybe I’d start with John.