Re: Lapping Rings
I generally check the ring fit first by installing & torquing the rings onto the rail, rec. etc. Then I put a little drop of mineral oil in the rings and setting the scope in. If it's a close fit, the oil will show a nearly even coat on the tube, then you can proceed with lapping, it shouldn't take much.
If something is really off kilter, like the base being twisted or cocked or canted by the receiver, you'll see very little oil coating the scope tube. At that point you can investigate the rail, rings etc. and correct that error before you lap the rings.
In theory, 'if' your rail is true on each rifle, there shouldn't be any issues moving the scope. You don't need to 'polish' the rings after lapping, the finish left behind by 220 grit compound is perfectly fine. Just make absolutely sure that you clean all of the grit from the rings, any that got on the screws or in or near the cap threads. Then clean them again.
Also, it doesn't take much lapping compound, if need be, add a few drops of oil to the lapping bar to make things go smoother, don't slather on more lapping compound. Lap a little, check a lot. It won't take much to true them up. It is possible to go too far, to the point that the caps won't tighten up on the scope but things would have to be pretty whacked to get that carried away.
When you set the top caps on, pay attention to the gap between the top & bottom ring on each side. Try to get it even before beginning the lapping process. Use a feelers gauge, doesn't have to be perfect +/- 5 thou or so is fine.
As you lap, rotate the bar in a figure 8, don't simply saw back & forth. There is kind of a rhythm to it. Keep gentle tension on the top caps. Too tight and you'll struggle with the lapping bar, too loose and you 'll only lap the bottom ring. Lap a dozen strokes or so & check/adjust the screws. The tops caps shouldn't flop around as you lap.
If for some reason you can't lap, it's generally best to install & torque the rings on the scope first, keeping the ring gaps even, then installing the scope on the base. The misalignment error will be imparted on the base instead of the scope tube.
I apologize in advance if some of this seems basic. The usual disclaimer applies, this is my method & personal experience, YM&TMV etc. etc.