I'm afraid I won't be much help here. I have the front bumper removed from my Argosy so I can't give an exact measurement front to rear. When I had the Argosy hauled from Arkansas to Kentucky I took great pains to make sure the trailer with Argosy was under 13' 6" load height for the interstate system. I know I was under that by a couple of inches and the trailer deck height was about 38".
I want to say my 20' Argosy was 10'-3-1/2" high to the top of the air conditioner with 16" wheels. The air conditioner was a Coleman Mach 3.
John, I'd say a 20' Argosy is going to be a tight squeeze in a 20' deep garage.
I do know that our 84 310 will fit inside an 11' high garage door opening with 4 to 5 inches to spare.