Two minutes seems fast, or maybe I am just not in that much of a hurry. I have a BX 24 and for me the challenge is getting the PTO connected. Short arms, awkward position, and quick release on PTO that closes if you look at it funny. Still putting the MMM on and off is not that big of a deal. For your problem I would start by removing the mower. Then I would separate the PTO shaft. Then I would try connecting it. With only the shaft, no mower in the way, it should be a pretty easy process. If it doesn't go on and off smoothly I would do more checking to see if the male or female part of the hookup is the problem. There is a chance it is just a matter of a good cleaning and maybe some burr removal. Keep us posted.
I have left my MMM on when doing dirt work, but don't like too, to much chance of getting it hung up on something else.
Take Care,
Doug in SW IA