Well I sort of had a breakthrough...sort of...
So I did the "shock" test to the oscillating module that mysteriously seemed to have fixed itself, okay? The thump the mic test...and sure enough it sent the module into oscillation again. I wasn't surprised, wasn't downtrodden...actually relieved because I just don't like problems that go away on their own...they're just hiding.
Then I thought "waiiiiiit a minute...most of the modules were doing this oscillation thing at one point, and then it was just 3 of them, and then just this 1...but suddenly this 1 isn't doing it...*unless I make it do it*." Do you see where this is going? I learned about the ability to force the oscillation without power-cycling the unit AFTER all the other modules "fixed themselves". So, right...you guessed it...I hooked the mic up to every other module and did the thump test and SURE ENOUGH THEY ALL OSCILLATE! Except for TWO of them...why not those two?? BECAUSE I SOCKETED AND UPGRADED MOST OF THE OPAMPS ON THOSE TWO MODULES AND BYPASSED THE POWER RAILS AT EACH CHIP on those two modules.
I think I'm are dealing with a design flaw here. It may have existed before and I just never noticed it because frankly I was focused on refurbishing and repairing other things on it, and only just this Spring did I engage in doing the in-depth full-function testing which is how I caught this issue. If it didn't do it before maybe it is only now manifesting because I recapped the modules with lower ESR caps and maybe the old caps were providing just enough HF damping to keep this from happening. SO...I guess I've got some experimenting to do.
I think how I'll proceed is to get enough new TI branded TL072 parts to replace all that are currently installed on one module (12 per module), as well as sockets. I'll start with JUST the EQ board, and one at a time replace the input amp, and then the output amp (the two that are still in the circuit when the EQ section is bypassed). If that doesn't stop it then I'll bypass the power rails at those opamps. If that doesn't do it I'll try OPA2134 parts in there (which is what's installed on the two modules that don't oscillate). If that doesn't do it then I'll (ONE AT A TIME) do the same process to the next amp in the signal path. If that doesn't do it after replacing all the opamps on the EQ board I'll work upstream in the same fashion, and finally downstream.
I'm hoping new TL072 parts and (if necessary) bypassing the power rails does the trick. I like how the stock modules sound better than the ones I already hot-rodded and I'd rather keep things relatively stock if I can. Once I rectify the issue I'll purchase the parts necessary to do the rest of the modules.
The only parts I'm really interested in maybe "upgrading" would be the 4556 parts (two per module) and the one 2041 opamp. I think I can probably use OPA2134 parts there...I believe the 4556 and 2041 parts were used because, at the time, they had the necessary output current potential to fit the applications (i.e. fader booster for instance)...70mA and 25mA respectively. The OPA2134 handily trumps the 2041 for sure at 35mA, but is only half that of the 4556...the 4556's 70mA max output current is uncommonly huge and I'm hoping 35mA will do it...gambling that Teac didn't really NEED 70mA but there really wasn't anything in between the 2041 and the 4556. I'm not sure of that but I have yet to run into anything that, at the time, was in between.
Anyway, I'm actually relieved that the issue is universal across all the unmodified modules...I'm much more comfortable knowing that this is likely a simple design limitation, and rather than searching for a failed culprit the focus can be how to manage the issue, which may be very simple.