I am thinking that your deformed caps are either a bad batch or you are seriously over-carbonating to deform them. Either way replacing the caps looks like a fix.
Did you have any really highly carbonated brews?
I observed some caps that had a definite convex curve after a few weeks of carbonation. I think the pressure was enough to deform the cap, breaking the seal allowing the beer to vent. Once the pressure decreased, it formed a seal again.
They should not vent from the caps unless the cap is defective. If they bottle feels firm, then it should not have a leak.
Sometimes a PET bottle will blow out the bottom (ask me how I know, then ask me again). Storing them in a plastic container (with lid) is a safe bet (ask me how I know that too).
I would just take the rings off and see if that fixes it, if not, try to isolate the bottles so you can tell which ones do it then replace them as you suggest. You could also try just using new caps (minus the ring).