Hmm. I haven't tried mecanim yet, but it sounds like you've definitely narrowed it down to mecanim being part of the problem. I hope someone with a little more knowledge about that can hop in and help out!
The only other thing I can suggest is, in Unity, select the animation that's causing problems, and then in the inspector, under the mini "rig" tab, choose animation type as "legacy". This fixes a lot of random animation issues for me, might be worth a shot.