Natural candidates for the hierarchy inside NPI
I've found a nice problem called ModularFactorial. Take as input two $n$-digit integers $x$ and $y$, and output $x! \mod y$. This problem is at least as hard as Factoring and not know to be hard for FNP. The reference is the recent (and beautiful) book by Cristopher Moore and Stephan Mertens The Nature of Computation, page 79.