I'm not one to disagree with John as he has way more knowledge on the transmissions than I do.
But will say it certainly sounds like a filter clogging up when running and then dropping some of the debris back into the pan which allows a short time for fluid to pass until it sucks the debris up again.
Fuel filters will do the same thing with a rusty tank. I would not be a bit surprised to find a lot of friction material in the pan and filter.
If my suspicions are correct, a fluid/ filter change may buy a bit of time but I wouldn't count on it lasting very long
good luck and keep us posted