1.000, +/- .003 is what I use. Drill rod works fine. The lapping compound will increase the diameter about .002. Most rings also flex a little when tightened, so a final ring diameter within about .003" of the scope tube diameter seems to work well.
I agree, solvent wiping doesn't completely remove lapping compound from the ring. I've found that lapping compound does comes off with Scotch tape, however. I first clean the ring with alcohol. I then lay a piece of tape over the lapped surface, press it in with my finger, then pull it off. Repeat and all lapping compound is gone.
I always use RingTrue tape after lapping.
RingTrue™ Tape for Three Scopes