I just bought a nice lapping tool from Sinclair. It's long enough to work comfortably and has a detachable "T" handle, also comes with lapping compound. Mine is 30mm and cost about $27, I think the 1" tool is a few dollars cheaper.
Just a point of info in case your piece of stainless doesn't work out. The handle really helps.
Also, if you buy some lapping compound you should get Aluminum Oxide, not Silicone Carbide. According to Sinclair, Silicone Carbide will get permanently imbedded into the rings and will damage the finish. The Aluminum Oxide that Sinclair provides is 280 grit.
To answer RemVSSF, even if the rings aren't lapped you still may have a perfect fit, but you may not. If not, when you tighten the rings down you can actually bend the tube slightly. It may still work fine, but personally I'd rather have a straight tube. In addition to insuring the scope rings are applying even pressure to the scope tube, one of the things I like about lapping is that if you ever move the scope to another rifle you shouldn't have ring marks from the first mounting.