I have run a TM and Hoses out the back a couple of times. Because they where set up like that when I purchased.
If your gonna be cleaning much carpet go with a side mount for the TM.
Front tire wear was always a problem. Rear mount gives you a ton of space in basically a square at the side doors.
Running out the side door gives you easier set up because the engine exhaust is away from the house.
Rear mount will blow exhaust same direction as your pulling hose.
370 should leave you a good bit of room if you mount it right at the side door. Mike has space beside his that would store all your janitor stuff I bet. Hoses out the back with carpet stuff beside the reels.