Assuming the issues with the loans are ok (i.e. there is no reason to think they have defaulted), and you seem to indicate they are indeed ok, then it boils down to how to get the loans and the money "transferred" into a new plan. In my opinion, that would require a plan merger (I don't know what "transfer" would mean otherwise). So that would mean establishing a new plan and then merging the old into the new. That is safest, in my opinion, as far as continuing the loans.
But here's a not-so-stray thought: why not just have the new company become the adopting employer for the existing plan? I don't see any reason not to do it and it saves a lot of trouble. The old company may not exist (or it may) but I don't think anyone will question the owner signing a consent to let the new company become the adopting employer.