[Yosemite Sam]

Regardless of your ultimate goal, I too would rather have the 3 point on the tractor with the hydraulic lift.

The 3 point will bolt right up to your 129 from the 1250, there is the possibility that your 1250 will not have part number 1 from your illustration but will have parts number 8 instead. If that is the case you will need to acquire a part number 1 (easy to make).

Hydraulic lift will not need the spring assist, best left on the 1250.

Some time ago I made an adjustable adapter for a ball because of the same problem you are having. I built it to connect directly to a sleeve hitch adapter, so that it was easy to move from one tractor to another or remove altogether. It does the job it was intended to do but is not rigid to the tractor (it wiggles around a little) the only trailers I ever needed to move with it are fairly light so I never feared any mishaps.