I still recommend playing with the blend (B, BT, T) knob set in either the T or B direction completely. Isolate this down to a single pickup and pre-amp, since they're separated for the most part. If the B or T setting squeals, but not the other, another easy test might be to very carefully swap the TAB1043 IC chips out with each other and see if the problem moves with the chip or stays with the blend setting of B or T. Use a small flat-head screwdriver to pry out each end of the chips (may have to remove the electronics from the bass cavity to do this).
If I had your electronics here, I could hook a scope up to it and see where the problem is happening.
Also, will it happen if you leave the bass alone on a guitar stand, plugged in and untouched? If not, then try plucking strings while it sits on the stand, being careful not to move it.
Lastly, have you considered having the bass re-capped (replacing all the old film and electrolytic capacitors)?