I'm envisioning a metal version that bears the load on the axle/ main frame, stabilized by the basket.
I would prefer it takes tow slugs so I could use it on my 4400 pound chipper that has a pintle ring, not only on ball couplers.
It's really useful to be able to manually spin the chipper for chip-onsite jobs.
It needs plywood or pavement, and isn't the easiest with the wheeled tongue jack, currently (I can do it solo, if I try).
One man could do it with the trailer dolly easier, I believe, as it would roll better, and have more leverage for spinning when attached at the end of the tongue. Two men, a breeze.
I can picture a lightweight "x-plate" laying on the top of the basket's round top tubes. It would have hitch tube(or possibly a round pipe sleeve for the BMG hitch) vertically welded in the middle-ish area. This would accept a piece of 2" tubing vertically, to which a piece of 2" hitch tube can be welded horizontally, to accept tow slugs.
This would need to be positioned with clearance for the stake pockets at the corner of the frame, and bearing the weight over the axle, as Marc-Antoine (is Marc your first name?) correctly pointed out.
I could imagine the "plate" basically being an X made from two pieces of flat bar and/or angle iron welded in the middle. Cut or grind notches on the end of the X that would butt into the stake pocket part of the frame, holding it in place. Probably needs a simple way of securing at two or more corners.
Possibly need to extend the round pipe on the BMG L-bracket tow hitch to the right length to rest on the frame.