The car whining is the clue, this means the transmission fluid control solenoids are clogged or the transmission fluid strainer is clogged with clutch material, and it causes the transmission fluid pump to scavenge which drops the clutch pressure causing the slip you have mentioned. I would remove the control solenoids first to see if they can be cleaned and if not, I would replace them, if this doesn't work then the transmission needs to come out and disassembled to check the strainer, at this point you might as well get a rebuilt unit. Check out the diagrams (below). Please let us know what happens.
Images (Click to enlarge)
Monday, August 29th, 2022 AT 3:09 PM