What are the complexities of the following SAT subsets ?
I think both are NPI under the stronger assumption (but obviously true) that NP is not in "infinitely often P" - i.e., every polynomial time algorithm A and every sufficiently large n, A fails to solve SAT on inputs of length n.

In this case, such languages are not in P, but they also cannot be NP complete, since otherwise a reduction from SAT to a language L with large holes will give an algorithm for SAT that succeeds on these holes.

Such an assumption is also necessary, since otherwise the languages can be in P, or NP-complete, depending on where the "easy input lengths" are located.