I know you can't make changes to the design, but there's no bypass cap on U1. All those guys should have a .1uf cap on all the supply pins. As for the USB 5V line...it probably would have been better to use a ferrite bead at the input or at least a better LPF.
And what a horrible datasheet for the TS462. They sure don't give you much, do they? I just noticed, are you actually talking about U2? I don't know man. You said you got the noise down below 100Hz. Are you know just seeing line noise?
The noise was broadband - see attached pictures which shows the spectrum with no input. It shows the low-pass nature of the filtering. Spectrum.jpg before my modification and spectrum_after.jpg after my modification.
Yes, the TS462 datasheet is awful.
U2B appears to be the problem with oscillation, but I've not yet fished around with the SA and detector loop.
The use of U1A is also questionable with a gain of -0.1.
And I've not yet got to the seemingly unnecessary AC coupling from the transformer to T1 - just return the transformer (secondary in this case) to VBIAS and DC couple it. That way, noise on VBIAS doesn't get added to the signal at this point. As it stands, noise on VBIAS at the + input of U2B is added to the signal at the - input.