The door Im not seeing as an issue but a problem that can be solved by a multitude of options. Height of opening is the restriction without seeing, changing door or type easy, changing the header not much more difficult-depending.  
But if you changed out the AC & if its enough to get under door it also would increase upward travel space, non issue. Might be combination of things to make it work. 
The real issue I see is if I could get into a 44'x64' shop and I could also have my camper inside- It would be real hard to ever get me out... 
Seriously though for that kind of shop space and getting the camper stored inside, Dolley/trailer would certainly solve although unless I wanted to move around it would be my last option, from here seems one way or another it could work.
Good luck