Can also tighten them rings to the scope first AND then tighten the rings to the base. This allows any slight misalignment to be moved to the ring/base connection where is will not bend the scope and allow the scope to fit in the rings for better grip and minimize ring marks on the scope. This has worked for me a couple times. Especially with steel ring and bases.
This is pretty much how I bed Talley rings on 'open' style receivers. After aligning the rings as close as mechanically possible, I torque the front down, and remove the rear.
Install set screws in the rear reciever holes (proud, to index the holes and prevent epoxy from leaking in).
Then set the rear base on the the receiver and tighten down ring clamps. I'll look at how much the rear ring base floats to estimate how much epoxy is needed, then remove front ring cap.
Remove scope (with rear ring attached). Apply release agent to receiver, epoxy to ring base.
Re-install scope (torque front ring cap). Let epoxy set.
Remove scope and rear set screws, install rear base, confirm alignment, install scope.
No ring marks. Less work than lapping.
No offense, Hand Skills, but your answer above makes me question whether you've really thought this through. And certainly makes me question whether you've actually ever lapped any rings
Good for you. This topic comes up on the forum regularly. I'm beginning to think my time will be better served creating a tutorial rather than responding to ad hominem.
Having honed and lapped many parts and many fits outside of firearms over the last ~40 years I have some experience reading the marks left by the process. Those marks told me that the rings were not round, but that the alignment to the action was reasonably close. Not perfect, but close. That is how I know, past experience with similar situations.
I have also lapped a one piece scope base to fit a Savage action. I did this by making a lapping bar in my lathe, and then lapping the base to it. Lap, check fit, lap, check fit. It was a simple but laborious process, but the fit of the ring lapping bar told me that the rings weren't the problem then.
I think it's laughable how many advise against it when they don't know anything beyond what the mfg tells them. Which may or may not be correct and is more likely how their marketing wants the optics of their parts to appear and their returns dept. being tired of dealing with rings that were lapped by someone with no clue. If you don't wish to do it then don't, but don't belittle those who do and can do it properly. Lapping isn't rocket surgery and it is a method to achieve a better fit, but it also isn't something that everyone should be doing.
Lapping has its place. It also has its limits. You talk about marks, and I hear you. What if there was a way to align parts, necessitating no lapping and leaving no marks? Taking your parts experience for example, when it comes to concentricity, ask yourself this; would you lap a bearing housing? Or would you index and sleeve it?
I'm sorry to have come across as belittling, in retrospect 'fools errand' may have been a bit strong.