I have an old Trek which has little adjusters in the dropouts to help with this. I don't think there is anything sacrosanct that says you have to have the axle seated on both sides. If your QR won't hold the wheel axle fixed with just clamping pressure, you've either got a bad QR or you aren't tightening them sufficiently. There shouldn't be movement in the axle with just clamping pressure and there shouldn't be any "wear" in this area.

The problem is that you really don't know if centering the wheel between the chain stays (or seat stays) is helping or hurting the issue. Is the problem in the basic frame geometry or in the dropout alignment? I'd certainly check to see if you get an improvement in centering with both the seat stays and the chain stays which would be a weak indicator that your problem is in the dropout alignment.

There are various frame alignment check procedures on the net, but I've never tried them.

I'd either live with it, or just make it part of your rear wheel mounting procedure to do the alignment manually. If you really think you get better overall frame alignment with the axle not completely seated on one side, then I'd look into some kind of shim. Perhaps JBWeld might work also. You could also look into carefully filing down the dropout slot on one side - either shimming one side out or filing the other side in should do the same basic thing. But again, I'd want to be sure that you're actually improving overall alignment and not just making it look better cosmetically. And as someone else said, you really want to be sure you're not reacting to a wheel dish issue or a bearing setup issue.

- Mark