I have an American Spirit AR15 in A2 configuration with a 20" heavy barrel and a pinned on birdcage type muzzle break.  I built the gun with an ASA lower and ASA upper kit.

The gun shoot very accurately even when compared to my friends Colt and Bushmaster but is extremely ammo sensitive.  PMC and PMP both stick in the chamber after firing and the case has to be driven out with a cleaning rod.  Upon inspection the case head shows damage where the extractor grabbed the rim and ripped off one side while trying to do its job.  This does not happen with Arms Corp, Sellier & Bellot, or some gunshow reloads that I have tried.  The much maligned Wolf ammo won't even cycle properly in 55gr loads but works okay in 62gr loads.

What can I do to alleviate this problem?  Is it chamber reaming time?

Have a gunsmith check your chamber and extractor. I would also suggest trying some Black Hills. You might also want to try different lots of PMC and PMP. Maybe you just had bad lots of those two.