Hey, I think that I figured out my troubles. It took long enough
I bought a cheap bore scope for issues with a different rifle (rust pitting from weather as it turned out, in the bore of my 20 year old model 70 elk rifle). On a whim I decided to scope all my rifles, and I eventually ran it through the 450 BM. The Saturn 450 bore is really rough, and takes copper like a cheese grader. Comparing the Saturn to the barrel on my cheap, 2 yr old Tikka (that probably hasn't had a full box of rounds through it) is like night and day.
With the rough surface, the first few shots aren't bad, but it fouls quickly. When you're constantly swapping scopes, those first few shots tend to be wasted to zero the scope.
I did a mild lapping with abrasive paste when I put it together the first time, but nowhere near enough to smooth this thing. I could give it a substantial (~80 passes) treatment, but maybe I'll send Satern a picture and ask if this is just how they roll, and find out what they recommend.