Does polynomially bounded number of witnesses and polynomial time decidability imply polynomial time enumeration?
Yes, you can do this unconditionally in $\mathrm{FP^{NP}}$, which equals $\mathrm{FP}$ by your assumption.

The algorithm is a version of binary search: if the witnesses you want to count are binary strings of length $n^k$, then compute by iteration on $i\le n^k$ the list of all their prefixes of length $i$. This list has polynomial length during the computation since there are only polynomially many witnesses in total, and given a prefix of length $i$, we can check which of its extensions of length $i+1$ are prefixes of a witness by an $\mathrm{NP}$ query.