Have you checked the transmission fluid? The level will change as it heats and I imagine could affect operation. It should really be changed if you're keeping the car.
It might also simply be overheating. The transmission fluid is cooled through the radiator. I think you said you replaced that. Make sure the lines aren't leaking or anything.
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The instrument panel cluster gauges seem to move in a manner suggesting voltage spikes, and this affects car operation. What could this be?
Are the headlights also pulsing brighter and dimmer, along with the dash gauges? Especially the voltmeter? My Pontiac did the same thing when I bought it.
It sounds like a bad rectifier. On GM's the rectifier is inside the alternator. I think Ford had it external for some years, I don't know about your car.
The alternator produces alternating current. The rectifier converts that into DC. If the rectifier fails you can get AC in the car's electrical system which makes the voltage pulse up and down. It's probably stressful for the power supply filtering in the ECM, and might also cause erratic sensor feedback.
I don't think this is causing your OD issue, but it should still be fixed.
From the way it acts, I'm wondering if you have a solenoid going bad on the transmission. This happens sometimes with computerized transmissions. I've never dealt with it myself but as transmission repairs go they're not so bad to replace. It might not be an internal problem.
You might research whether there's a solenoid in/on your transmission which is responsible for engaging OD and fits your symptoms. If so, find out if there's some way to test it and what's involved in replacing it. If this repair is feasible, then it should probably be done at the same time as a filter and fluid replacement. Clean off the magnet if there is one. Adjusting bands would also be good, but if you don't have the tools and good instructions then leave it alone.
When it loses overdrive, does it still try to go in and slip? Just in case, to be safe, I'd lock out overdrive when it isn't working.