I am not sure of exactly why they do this, I think it is because in 3rd gear it has a sprag holding it, and will freewheel when you coast, or, when you let off the gas, the torque converter lockup clutch is disengaged.
My 89 Notch did the same thing.
It may be that the solenoid is inhibiting od application, but that's a long shot.
I simply put a used $100 trans in mine and its worked fine for 3 years now.
I don't think flushing/fluid change will fix this problem, something has failed.
Obviously you can rebuild it. This trans is not as bad as people make it out, it's just that it was sold in the baseline transportation oriented cars, and never got much care or thought. It is the same basic trans that is in the 08 Mustang GT's, with 300 hp....
Maybe this will get it some aftermarket support.