BillR, Sorry to hear about having to miss your hunting trip. I believe that BH has nailed it.
Did you anneal your cases after fireforming? Cases will always spring back around 0005 after firing, and if they need annealing they sometimes spring back much more. (or maybe dont expand sufficiently on firing)
A simple test which I always perform before reloading a fired case is to slide a bullet down into the neck, if the bullet passes freely, then the neck anneal is ok. However, if it is either partially or fully restricted then I put that case aside for annealing, which I find solves the problem.
Only having .003 neck clearance, means that you have little margin for error in your reloading procedures.
I have a similar problem to you in my .224 Clark. The chamber is .2543, and my loaded round is about .2520, (necks .014) so I only have about .0023 clearance. My RCBS neck sizing die only reduces the case necks to about .252 (or a tad less). So due to differences between cases, about 20% of my cases do not have enough tension to securely hold the bullet. However, if I full length size the case, the neck is reduced to .250, which is sufficient to secure the bullet on all cases. Rather than use my F/L die each time, I intend to purchase a Redding S Type with a .250 bushing.
Once you get these minor problems, sorted out, I believe that you will love your 25/06AI. Good luck. Brian.