Only thing I can think of is a slipping belt.

I don't know if this is the problem, but inherited my JD, and it came with out a brake. I lived with this for several years but then bought a new house with some slopes and it became a problem.

I finally found the problem. In the place where the brake apparatus goes through the frame channel there was a collection of debris, that could not be seen in normal ways. Once I found it and cleaned it out every thing worked fine.

Do you have a similar problem? Debris in an unable to be seen corner preventing the brake from completely releasing, or preventing an idler pulley from working properly.

May be a with debris interfering with its operation?

I could understand debris not letting the brake return to it's max position. Will try to clean out around the linkage really well and report back with the fix.

I had a similar problem with my Craftsman tractor. I too changed the fluid in the transaxle, the belt (at least twice), lost most of my religion and all of my temper and eventually abandoned the mower to a back corner of my barn. Later, on a whim, I ordered a new main pulley (sheave) and installed it on the engine shaft. I could not believe the difference!!! The problem was SOLVED. Hope this works for you.

Try running it with the fuel cap off.

Maybe I am not reading your symptoms right but it sounded like you said, after you did your transaxle work that it ran fine for about 20 minutes and then it would stall every 30 to 50 feet, even on flat ground.

Is it possible it is a fuel starvation problem that exacerbates itself when it requires higher RPMs for hills or just overtime.

I guess we should ask which definition of stalling the OP is experiencing.
Stalling as in "engine RPM stays high but the tractor stops moving"?
Stalling as in "engine quits running"?
Or, stalling as in "engine RPM drops so low that the tractor stops moving"?
Of those 3 scenarios, only the first would be due to faulty performance by the transmission.

mownie: Stalling as in "engine RPM stays high but the tractor stops moving"

I managed to solve it. Turns out that topping off a T-2 is more involved than I thought. (Transaxle was shipped FedEx, and arrived with a light coating of oil. Probably came out the overflow breather as it was tipped).

I pulled the transaxle off the mower after my prior post. The oil was to the bottom of the threads. However, I went ahead and filled the threads to the brim. I had the oil... why not? After about 10 seconds, there was a bubbling action and the oil went back down to the bottom of the threads.

I repeated that process 4 or 5 times. Then I proceeded to hand-turn the pulley, which helped pull the oil down. I alternated between turning the pulley and adding a thimble-full of oil each time, occasionally stopping to switch the bypass on or off.

Once this was all done, and the transaxle reinstalled, it didn't stall once. I would guess that I added 2 or 3 ounces of oil after it was already "full".

So there's my solution. When you fill it, exercise the pump on the bench before declaring the job done.

I am glad to learn you were able to get it going and not the owner of a defective new trans.