How far from having a plausible keys are you to finding the actual key that corresponds to a public key in general terms?

That I do not know for sure, but my intuition tells me that we can get closer if we first use GAN, because it may shrink the distribution space. It's just an intuition now, like I said I lack the mathematical skills (or the time) to model properly.

It may even be a question of trial and error until we find which parameters in the learning process affect the validity or the probability of finding a working key.