Andy, to be frank, I think it might be best to cut your loses and just stick with previous amplification methods that work better for you.
Sounds like you've given the Axe more than a fair try, and it appears to have brought you nothing but ongoing difficulty. You've had post after post on this forum with technical limitations of the unit, complaints about the sound quality, statements of how everything sounds the same, and an apparent lack of fundamental knowledge of how a digital modeling device works.
The Axe is a great unit, but its not one size fits all. You seem to be an established player, and know how to get tones you enjoy out of previous gear you've been using. I think there gets to be a point where new gear simply might prove to be more trouble than its worth.
How much time and effort do you want to put into trying to learn something new, which still might not prove to your liking, verses falling back to using a rig that you and your engineer are happy with and actually spend that time laying down some tracks ?
I know the Axe was a considerable investment, but if your still not getting good tones, after all the various help you've gotten from forum members in different post, maybe its time to try something totally different ?