I spoke with Dr. McBride about this yesterday since I felt that I only knew part of the answer.
Mashantuckets would not have appeared on national censuses during this period nor would they until about the turn of the 20th century. That being said, the overseers did at irregular intervals take a sort of tribal census where they counted and listed the families living on the reservation. There is one of these in the early 1830s, I believe. Some caveats about this: It was not a true census and provides very different information about the families than a national census would. Also, the lists are not considered to be complete and it is very likely that some families are left off. This could be for a variety of reasons including racial bias or perceived inauthenticity on the part of the overseer or other Mashantucket community members.
If you are interested in learning more about the overseers or the tribal lists, Jason Mancini is a good person to talk to. I can also help in any way I can or of course Dr. McBride is also a good resource.