Validate per round rather than cycle-walking in FPE
I don't think this would break correctness, but it's possible you might actually slow your algorithm down on average. You'd need a more rigorous combinatorial analysis of the expected number of repeated rounds vs. the expected number of full cycle walks. That really depends on the specific algorithm; are you using FFX?

You'd also need to show that doing this doesn't alter the distribution of ciphertexts in a way that breaks SPRP security. It's possible that it doesn't, but proving it seems nontrivial to me.