After posing the problem to a buddy, we've come up with an idea. It's completely unnecessary and will more than likely be a huge waste of time, but we get to fabricate stuff for the fun of it. He works in a robotics shop. Another buddy buys junk four-wheelers (quad bikes to the chaps across the pond) and parts them out. He's got a stack of rear swing arms with the axles still in them. We're going to take a swingarm, rigid mount it to the axle and back bone of the AT, put an electric gear reduction motor above and in front of it and use a 12V deep cycle battery to run it. We'll replace one of the hand grips with a twist throttle off of an electric scooter for the speed control. The four wheeler tires are 8-10" wide, so they'll take care of the sinking in/flotation problem. The electric motor will take care of the extra drag of the larger tires plus the extra hundred pounds or so of swingarm, motor and battery and generally make life easier. Think of it as the Tesla of Arbor Carts...
I'll take a hundred pounds less capacity for not having to drag half a ton of weight by hand.
Or we'll waste a weekend, have a lot of fun tinkering, drink a few beers and put the AT back to stock.
Either way, time well spent...