Well yes, there is another explanation that works. It's called superdeterminism. Unfortunately it's non-scientific. If that is what you mean (as it seems to me) then it's no real alternative to FTL.Another approach is to simply say that the measurements done on the system are part of what determines the probability distributions of those measurements. This is, after all, just what we see with entangled systems, it was only ever us that said these systems had to comprise of independent probability distributions. We know they do not, so why force "influences" down their throat, when we can just say what we see to be true: the probabilities depend on the measurements we choose because part of what we mean by the system is how the outcomes of chosen measurements interact with the preparation. That's really all physics ever concerns itself with, the idea that you need influences to alter the independent probabilities is merely a holdover from other contexts where that actually works.
First of all, entanglement is never about perfect correlations, because you don't get Bell violations with perfect correlations. But a more important issue is, I never said the theory doesn't violate locality, of course it does that. I said it doesn't need to violate it by application of a concept of "FTL or retrocausal influences." One simply says that to talk meaningfully about a system, we need more than its preparation, we need to know what attributes of that system are being established by measurement, and the probabilities it will exhibit depend on the way the measurements establish those attributes. Again, outcomes are an interaction between preparation and measurement choices, no influences needed, FTL or otherwise. I'd say that same thing even if the speed of light was infinite-- there's no magical "influence" there either way, its causality violations are just a good clue we made a bad choice of language.
Btw As you refer to FTL and retrocausal influences together do you consider them equally unacceptable?