In my experience hkpistole may be on the right track to solving your problem.
Check to make sure the screws are the same length & in appropriate holes. I have seen where screws that are a fraction longer can cause this type of problem if they are put into a different hole that the one they came out of.
Additionally, if a screw is slightly bent (at the head for example) it can wreak havoc because as you begin to tighten the slightly bent screw it can put differential pressure as it seats under pressure of tightening (very small difference in perceived tightness = large change because of a bent screw) especially true on pivot screws, blade stop-pin screws, pocket-clip screws (ones that screw into a liner near the pivot - Para, Millie, etc.).
Also, debris (dirt, residual lock-tite, etc.) between the scale and the liner and really cause great frustration during final assembly tightening.
Re-reading your post again, it sounds like when you are tightening the pocket-clip screws they are either causing the liner to flex, or putting pressure on pivot. This can be caused by a number of things.
Re-reading your OP again, I should have first asked which is/was better:
1. "before hand the centering was FAR from ideal."
2. "I attach my clip and the centering was at maybe 20%. Terrible, but still smooth."
3. It's the same