Oh, so it's the hash itself that must be less than a specific value, not the preimage of the hash. Still, that can be rephrased as "inverting any one of the hashes that are below a certain value", which is why I kept mapping it to a hash inversion problem.

And the only known way to do this is to try a large number of bitstrings and see what their hashing yields? Is there a known way to more efficiently search by looking what what bitstrings are likely to have hashes with zeroes in the most significant digits? Could someone improve performance by finding such a method?