I have some questions. How much tighter is the diff getting after a run, does it get like really really tight compared to at the start, and is it possible that it is slipping?
It would make sense that heat would be the problem because as the balls roll (or slip) they are generating heat which leads to expansion, which could cause the tightness.
Depending on how tight you have it set up to start out with. You should have it the loosest you can without it slipping.
Steel diffs are probably a little more precise than plastic outdrives (you are running plastic on the rear, right?
Locktight probably wouldn't solve the problem but go for it.
Definately buy an X-ray, especially if you want to have to wait 2 weeks for parts or have a cars-worth of spares with you.