Ruger Scope Mounting

I posted this in the rifle section, but think this may be more appropriate here. Sorry for the double post...
A novice question here! I have my Ruger Hawkeye .270, I have my Sightron 3-9x50 scope, and I have the medium rings that came with the rifle, as well as the high and extra high rings that Ruger sent me. A couple of questions for you Ruger experts out there. When reading about mounting a scope, a lot of time is given to proper scope alignment with the rifle. Does this apply to the Ruger? Since it has an integral base, I don't see how the rings/scope could NOT be in alignment, and how it could be fixed if they were not. Second, the instructions that came with the rings say that the ring top and base are a matched set, and CANNOT be mixed. Unfortunately, I didn't read that part until after I had taken them off and mixed them. I cannot see any difference in the two caps, so I have no way of knowing which cap came with which base. Is this concern unwarranted, or is there a solution?

I'm not sure what to do with the rings, other than call Ruger and ask for more, or just go buy some. Since I've mixed up the top half of the rings (i.e. don't know which top went with which bottom), I tried every possibility; I've tried each of the two tops with each of the two bottoms, then turned the tops around and tried it that way. The problem is that the tops fit the same no matter which way I try it, and they DON'T fit like everyone says they should. If you sit (or screw down) the top on one of the bottoms, the inside edges of the tops where they match up with the bottoms are slightly wider, meaning that if you run your finger down the inside edge of the ring, you feel a ridge on either side going down. It's not a major ridge, but all feedback I've gotten so far implies that it should be pretty much smooth, with no ridge.

I mounted the scope, and tried to sight it in, but cannot get anything consistent whatsoever, making me think it's my mounting, rather than the gun or the scope.

My next stop will probably be to a gunsmith, unless someone has another thought or idea that might help!

I would recommend lapping the rings. I do this to all of my scope mounted firearms. If done properly, it won't hurt the system, even if it turns out to be unnecessary.

You're gambling that when Ruger machined the mounts into the action, that they got them absolutely perfect. You're also gambling the same thing on the rings. Both of those together rarely happens.

Your accuracy problems could also be due to a ton of different things: your rifle doesn't like the ammo you're feeding it, the action isn't torqued properly, the rings aren't torqued properly, the scope is bad, etc.