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I have done many transmission myself and believe I know how you feel. To my mind you are on track. Can only be on the inside the transmission. The high temperature could have destroyed the solenoid windings and or the wiring harness.
I think if you feel that you need to check the pressures then do that. But as you say you know that the fluid got very hot so I think the solenoids has all taken a beating.
I have been thinking about your question and you say after you first repaired the cooler and replaced the fluid the car ran fine. So that to me say that the clutch packs has to be good. It must be something to do with the solenoids. or the wiring. The brass clutch packs do not wear very easy I has seen the transmissions on fork-tucks taking a severe hammering before they go bad.
I would check the solenoid first and make very sure they are good.