Looking at your spectrum analysis the form of the peaks is very characteristic of a low level square(ish) wave. the fundamental frequency is at the mains power frequency, so the cause of the problem must be the power supply. The cause might be ageing of the smoothing capacitors….. there are two 470uF capacitors in the 15V regulator circuits; it would be worth replacing these with 1000uF 40V caps. Another possible cause could be the phantom power generator, but this is a bit more tricky; I doubt if it is worth replacing all the electrolytic caps, but the main ones in the power supply will probably fix the problem.
BTW, can you hear it??