I have an eternally full tank!!!

Rather than crawl under to get to the sending wire, remove the driver's left-foot kick panel and unplug the ~10-pin connector. That is all wires to the rear, including the sender. Most likely a shorted sending wire, or a shorted sender, is your problem. From the connector, you can test all. Measure the sender resistance, or install simulator resistors to go the other way to your gage. You will need a wiring diagram (search here) and some alligator clips, and a free HF multimeter.

I 2nd your exaperation w/ "professional" mechanics, and why most here do their own repairs. Your issue is very easy to diagnose, and even easier in your old model. I don't think the fuel gages in newer cars work any different, like have become digital, but could be wrong. They sure are harder to get to. I will probably be pulling the fuel pump assembly in my 1996 Plymouth this weekend (suspect bad fuel pump), so I'll look at its sender.