I assume that engine is sleeved ? No matter because if all it is a set of rings and a rework of the cylinder head that has to be cheaper than a rebuilt engine .That is providing the cylinders are not shot ,bearings etc .
If it runs as well as you say it does it can't have that much wrong with it .
Now this idea of running it so hot it took the temper out of the rings doesn't sound right because had it gotton that hot it should have cracked the cylinder head .
Pull the head and take a peek at the cylinders .It they are worn and eliptical you obviously have some big problems .If you roll it over and the rings don't wipe down the cylinders that will pretty much tell a tale .