Well, he does name one of his children Solomon (as per 1860 census) which is a very big clue.There is an Augustin Pace in Quebec in the 1851/52 Canadian Census, aged 30, living with an Elizabeth Pace (maiden name) and Charles Barribeau, but he may have simply been visiting, altho' they were to have noted that on the census form if that was the case. Women in Quebec maintain their maiden names even after marriage.
You are best to try and find the marriage in Rhode Island (likely) or the baptism of the oldest children in Rhode Island which may provide clues (ie, sponsors, etc.)
Other children of Solomon were Luce, Elizabeth & Solomon. Have you tracked down the rest of them to see if you can find a connection?