are you sure? it could be that you know that it's signed by A valid key, but not know which one. I really don't know how this sort of "many signing keys, one verification key" setup works. I'm interested to learn.
I am assuming that this is an asymmetric key, and so knowing the validation key does not let you know the signing key. If that's not the case, all you would need to do is to seed a PRNG and use the output as your symmetric key along with a generation number. That wouldn't be nearly as good as as if this is an asymmetric key.
your 'skip time' log entry does you no good if you don't have logs from all time (what happens when you delete the 'skip time' log entry), you would have to chrun thorugh however many key generation cycles you need to get you to the valid key (and hope that time never goes backwards on your box) as was noted by someone else on this thread.
we can speculate and design what we think is a valid algorithm here, but we don't know if that's what's being implemented in this case.