:welcome: to iBoats . . .
The short answer is yes . . . A fiberglass floor with foam backing encased in fiberglass is a way to go. Others may have some additional suggestions. The challenge will be making 'the sandwich'.
After you have a few posts, you can post pictures so that the folks here can better visualize what you are dealing with.
Also, I would triple check those stingers, bulkheads and transom. Lots of folks rip up the floor and think the stringers look/feel OK, only to later find out that they are not.