When you say "all you have to do is document the second 337" could that be as simple as a forms entry stating that it was completed?

An IA, AP or the FAA can go through the log books. There should be a 337 done by whoever did the repair you mentioned a few years ago.

In return, the inspector can just make a entry stating “ACFT was repaired on MM/DD/YR by repairstation #. See attached 337 for documented maintenance done at that time. ACFT was reinspected and found to be in full airworthiness standards IAW Part 43. Blah blah blah.

Really not a big deal. Just figuring out the paperwork is the biggest thing. There could 100% already be a entry in a logbook somewhere covering all this and there’s no action needed from you right now and everything is legal.