I figured you guys were due an update.
I did inquire with several places, including the one in the thread above. They were...expensive. Very expensive.
The guy I bought the manual from on E-Bay repaired these back in his working days. He's now retired and lost some of his eyesight so he can't work on them anymore. He has however been a wealth of knowledge.
I performed all the troubleshooting in the cassette manual, all was well. I consulted with him and he said his next move would be to replace the tape mechanism. He happened to have one which he sold me for really cheap. It came and I put it in. I would not recommend someone who doesn't have some electronics experience trying it. I do have some thought, and it was moderate difficulty. There is a 7 pin connector to de-solder and re-solder on the board, and then a 3 conductor wire with the signal from the tape head that gets soldered directly to the board.
Anyway, got it all installed and put it in the car and.....oh no. That dreaded "I let the smoke out of the electronics smell." Drat.
More troubleshooting and I discovered I had a solder bridge between two pins on the 7 pin connector which made a short straight to ground. Inspecting the board I found a blown out trace, turns out to be the trace brining power in from the battery. It was under the main power supply capacitor, which I don't think was damaged but was burned on the bottom.
Fixed the solder bridge. Ordered a replacement capacitor from Digikey. Fixed the trace with part of a connector pin. Installed the new capacitor. Take #2 in the car.
The AM/FM radio works as good as ever! Yay! I didn't blow too much stuff up. However the new cassette deck has.....exactly the same behavior as the old deck. The unfortunate conclusion is that the problem is not the TN-707 deck, but rather something to do with the tape circuitry.
The helpful e-bay man sent me a picture of the schematic for the tape section of the board. I inspected that section, looking real hard at the capacitors in particular. I can't see anything obvious wrong, no bulging capacitors, no corrosion. I know what the next step would be, powering it up and using an oscilloscope to figure out which component is bad. But, that's now beyond my comfort level on something this complex.
This whole time there has been a radio on E-Bay. It's the proper radio, same year. It is the one that goes with the graphics equalizer, but the seller didn't have that so it wasn't going for an arm and a leg. I decided to pull the trigger before it disappeared as these are extremely rare. It came, is in excellent condition and more importantly.....
It works perfectly. AM/FM and Cassette are all clear as can be. No hiss, no noise. Radio problem solved.
I am going to try and get the old one repaired. I think the guy who sold me this one refurbishes them so I've asked if he can fix up the old one.