A M1061 would definitely handle the load and brakes are air over hydraulic so that is a match as well, but the height and lack of ramps are the primary issues. I had a M1061 and it was great behind a deuce, but high for a vehicle load.
Remember, they put a complete laundry unit on it including huge stainless washers and dryers, a 10kw generator, hot water heater thar was a multifuel, spinner, water pumps, overhead racks full of piping, electrical. Walkways and lots of other stuff.
It was actually over 10k net weight. Cheapest way to go if you can make decent ramps and a way to mount them.
I just loved that trailer!
The other option is to add a mount for a ball hitch and use a civilian trailer.
I've done that too but relied on my towing vehicle for all the braking.