Gees, you guys are making me blush with all of this attention!?!
Unfortunately, I don't have access to year specific info on yours to be precise with my accessment and diagnosis, so I will have to rely more on practice and earlier setups, but they should mostly be the same. I would need Rod to validate some of this, but first off, basically the sunload sensor helps the electronic temp controls figure out how to compensate the inside air temp for the sunload detected on the car. Ford says it is "located in the right hand upper outer finish panel" for a 95. After translation and verification on my 95, they mean in the top of the dash at the windshield. There are two identical locations for this thing in my dash, with my sensor on the LEFT, driver's side. I'd think even your year would be similar. If not there, then probably under or in the cowl vent area. Since the sunload sensor plays a role in the EATC cooling logic, it's conceivable it's your problem. As Rod said, your symptoms are strange and inconsistent with normal faults. Which for me, makes sense to have a bad electronics "smell" to it. Anything that seems to defy a reasonable explaination seems to lead to an electrical/electronic problem. Since you said the self test indicates the sunload sensor is open, you could verify that yourself with an ohms meter with it disconnected. If not open, there is a special resistance test that can be done, but it's something probably more familiar to Rod than me, due to it being a photodiode.
Like Rod said, I don't get you jumping the low side clutch cycling switch getting fan but no clutch. That doesn't jive with the sunload sensor problem. I'd have to see the wiring diagram on that. Possibly the PCM is being told by the EATC not to engage the clutch. You would have to completely bypass the clutch wiring with a hot and ground to verify if it works. Looking at a similiar year diagram, you possibly activated the low speed fan when you jumpered the clutch switch, because the PCM sensed the power supplied for the clutch. With that particular diagram, that is the only way the low fan could come on with the AC. The high side sensor/switch has four wires, usually by the compressor, and can turn on the high fans with a jumper to the correct pin holes. The other two are for shutting off the ac when too high pressure occurs, and will allow it on when the pressure is low enough.
The pressures you measured while it's running sound good. The 125 psi is posssible if it's hot outside. I'm more concerned why you felt you needed to add refrigerant originally. Was it not cooling very well? Try running your car in a very well shaded place to see how it works, possibly taking the sun sensor out of the equation. I'd like to know the temperature of the cold air, at max cool and fan speed. Look underhood for heavy sweating and frosting. Don't want lots of frosting!!! If you overcharged it, the high pressure cutoff would turn off the clutch, but should let it back on when it cools down and pressure equalizes. When it would stop working when hot, did it ever come back on, even after cooling off?
The thought of a bad coil is "chilling" as I had to change mine and was determined to do change in the car so I didn't have to discharge the system. Rod may be right, it is possible the coil "can't stand the heat" and a broken wire inside looses its connection when it gets hot.