Motivated by these posts, [An NP-complete variant of factoring][1] and [Relationship between symmetry and computational intractability][2], It seems to be worthwhile to investigate the different factors that increase the hardness of problems in NPI. I'm interested in other NP-complete variants of problems of intermediate complexity. Is there a recent survey paper of NP-complete variants of intermediate complexity (between P and NP-complete: NPI problem) problems?

[1]: http://cstheory.stackexchange.com/q/4769/495
[2]: http://cstheory.stackexchange.com/q/871/495