Next thing I would try is disconnecting the kickdown solenoid at the transmission. It's the single wire going into the very back of the tranny, on the passenger side. What happens if you drive the car and let it wind up to 5000rpm in first gear? Will it upshift, or stay at 5000-5200rpm in first gear? The fluid level sounds acceptable.
The kickdown solenoid *might* be stuck, and yes it can be replaced externally... ATF will drip out while its removed though. BT, DT. I had a faulty solenoid, not a faulty valve... mine wouldn't kick down at WOT. That's the opposite problem though.
If the kickdown valve is good, it sounds depressingly like an internal failure, meaning a rebuild could be in your future.