DON - I'm sure Aaron will help. But take a look at "Pronovost" in a google search. I tried posting a link but for some reason can't capture it! I have their #P503 tandem cart. It has a 3" x 12" cylinder, the bed is 50"W x 70" L x 18" H, it has sideboards added by the prior owner. My 982 can lift it full of crushed rock up to the top of the steel sides at an idle. OHHHH, and the best part is they're made in Quebec, CANADA.
The box is set-up different than your cart, it pivots from the back so the very back never gets close to the ground unless the tailgate is dropped down like a pickup tailgate. It also unlatches from the bottom to dump like a normal dump truck box too.
I'm thinking a short cylinder, say 6-8 inches long set between where the two angle irons drop down along side the tongue at the front of the box, running back towards the cross member just ahead of the wheels/tires would dump your cart. The diameter would depend on how you load the cart. If the frt was filled to the top without the tailgate in it would take more force to dump, a 2" dia cylinder may not dump it, but a 2-1/2" would I would think.
My cart only raises to about a 45 deg. angle, and it really doesn't clean out as well as I'd like, I think 55-60 deg. would be better. But I pull it with the 3-pt to sleeve hitch adapter with a real short drawbar so I can raise the hitch level and it works much better. Hitched that way the weight is further back on the tractor, enough so the frt wheels barely touch the ground and I have to steer with the brakes.
I've used my cart a L-O-T with the 982, and there's only been ONE load of dirt last summer I couldn't raise, the tailgate was off, or at least down, and the cart was loaded with loose dirt heaped up to over-flowing across the frt and most of the sides, and I had to hit the hyd. lever while backing up then jerk the tractor forward to get the cart to raise. On one other load I had to speed the engine up to a fast idle to raise a similar load. I bought it slightly used almost 2 yrs ago for less than HALF what Northern Tool used to sell a similar cart for. My only regret other than this one not raising quite steep enough is that I don't have a much bigger one to pull with my FARMALL's, I'm thinking like a 10K or 16K size, something I could pull with a truck or a tractor.