For stuck parts, try a soaking in mineral spirits, (paint thinner), followed by another soaking in transmission fluid.
The combination of first soaking in a solvent, followed by another soaking in a good lubricant seems to work.
A little judicious use of force might still be needed, though.
Walt Kelly, alias Pogo, sez:
“Don't take life so serious, son, it ain't nohow permanent.”