Couple of things that you may have already checked, but...
Front scope base screw(s) long enough to touch the barrel shank? Thus can make a screw seem tight, but still allow a tiny amount of movement.
Bolt handle contacting the stock? This can make strange things happen, too.
Bolt nose contacting the barrel? You said the headspace is tight, so I'd check this. I had a Savage PTA rebarreled with "zero" clearance between the bolt nose and the face of the barrel. Shotgun patterns. Backed the barrel out, easy to do with the barrel nut, torqued it back down with about a thou and a half clearance. Groups shrunk to 1/2 MOA or less, and were consistent, no more weird flyers.
