I think this indicates a failing transmission fluid pump, a trans export
will
no doubt correct me, but as I understand the theory, as the trans fluid
gets hot it gets thinner and less viscous, and a trans fluid pump that is
worn has a lot of clearance, thus cannot develop adequate pressure
to shift when the trans is hot.

I suspect that the fella had a blown-up transmission and so did the
time honored deal of going to a u-pull-it wrecking yard and getting
himself a boneyard trans, that after doing all the work to install it,
he discovered this problem, and so ended up just giving up on it.  I
suspect the jack letting down story is a big bunch of baloney.

Ted