Slight hijack. Most (but not all) action tops are curved to some degree. Most bases are curved to match (ideally a bit smaller radius of curvature so the bases do not touch only on a line between the screws, but on the outside edges.) When you put two surfaces like that together they tend to have a single "best fit" orientation. (I'm simplifying a bit, but not much.) Even if one can get the rings to line up while tightening the base screws with the rings on the bases and held in alignment, this has never seemed to me to be a very robust or stable arrangement. But perhaps it works well enough most of the time.
This is the reason I epoxy bed my Talley lightweights to the receiver and do not have to lap them and end up with near perfect scope to ring alignment.
Cut off the heads of 4 mounting screws, coat lightly with wax or a release agent, Wax the top of the receiver and thread screws in with 1/8" to 3/16" sticking out.
Place rings on receiver over headless screws and mount your scope or a virgin lapping bar. remove the scope/ring assembly, thoroughly clean the bottom of the Talleys where they contact the receiver.
Mix the epoxy ( use regular epoxy or bedding compound, not 5 or 15 minute stuff) and coat the receiver contact area of the ringmounts and put the scope/ring assembly back on the receiver over the headless screws. Apply large rugger bands, surgical tubing or electrical tape to hold the scope tightly to the receiver.
Let the epoxy cure for 24 hours.
Tap the scope/ring assembly on the sides of the rings with a taped brass drift punch to break it loose and remove it. Remove the headless screws.
Clean the receiver, new receiver screws and scope base holes. Remove the scope (or lapping bar) from the ringmounts.
Apply blue Loctite to the new base screws and mount and torque down the lower ringmounts being careful to mount them in the same position and orientation as when they were put on with the epoxy.
Mount your scope with the tops.
Now you have as close to perfect ring/scope/base alignment as you can get and without lapping your rings. RJ
