Conventional wisdom seems to be (1) that doctoral degrees earned online are less exciting to brick and mortar universities than ones earned traditionally, and (2) there's a bias against proprietary schools in general and Phoenix in particular. Neither of these are justifiable in my opinion, but you'll face them if that's the path you take. That said, someone must be getting what they want from these programs or else no one would keep doing them.
If you teach for Axia, can you get an insiders perspective of how grads of the EdD programs have tended to do? That's what I'd try in your situation.
-=Steve=-
B.S., Info Sys, Charter Oak State College
M.A., Educational Tech Leadership, George Washington University
Doctor of Health Education, A.T. Still University, in progress