TPS rings fit like a glove, no room for lapping grit. It wasn't that you overdid it, as you found out it shouldn't get done at all with true rings and bases.
When I install them, I get the rings positioned and lightly snugged on the rail and snug the rings to a bar that is exactly the same diameter as the scope (No Grit!), careful here, lapping bars are often bigger and it sounds like yours is true of this...then snug the rings to the base, then tighten the rings, then tighten the rings to the base. I feel there is more potential for slop in the ring to base fit and if you tighten them on there first, there is a chance that it will be misaligned when you go to drop your scope.....or bar in. Once all is tight, remove the bar, install the scope, leave the tightening side of the rings loose enough to rotate the scope if you need to. The TPS rings are made so that one side is hard up tight and the other side does the clamping.
You could file down the mating surfaces of the cap and end up with a lapped leupold class ring fit, but a new set of TPS rings would fit much better untouched.