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Your ring halves are supposed to have gaps between them. Don't try to make them close. Just make the gaps even.
You can easily lap your rings by putting a small amount of jeweler's rouge or Flitz on a metal bar the same diameter as your scope tube and rubbing the coated bar in your installed rings to smooth out the burrs. Be extremely careful to remove all traces of this mild abrasive, and take caution not to get any rouge on any firearm part. When you are done, you can see the shiny places where the high spots were. This gives a more secure purchase for the rings to do their job, and firmly hold the scope.
Shimming bases is easy. Cut shim stock from a steel or aluminum can slightly smaller than the size of the base, and punch holes where the screws will go. Raising a base will give elevation that does not require your scope to be too far off center, its strongest point.
The more you remove and install turn-in rings, the looser they get.
When snapping the tight fitting top halves of rings over your scope, insert a dollar bill between the pieces to prevent scratching the scope. The bill is then easily removed.
Remember, your scope mount is the weakest link in your shooting system.
