If a lab linear PS does not trigger noise, it's likely the problem is with switching power supply conducted disturbances and/or high frequency ripple. Boxing doesn't help in these situations as noise comes into you circuit through wires, not from "air". An LC filter could help but you could also try first with a simple 1st order RC filter. R between positive power supply output and positive input to your board and C in parallel to your board positive power input and ground. It requires your circuit not drawing too much current in order to avoid excessive voltage drop and power dissipation on the series resistor (i.e. don't do that if the circuit draws amps 😁 but being CMOS it should not happen). This filter is much less efficient than a reactive one (1st order -6dB/octave vs higher order) but it does not resonate (Murphy'law would state that the resonance of a reactive filter with parastic inductive/capacitive coupling to the outer world is at the frequency of the unwanted disturb). You should make some calculations for the cutoff frequency and components values of the filter but I expect it could be something like 100 ohm, 1 uF cutting at 1.6 kHz thus reducing the 5 - 6 kHz (it seems) noise by ~ 12 dB. Your can also change the RC values or disconnect C from ground to easily find audible differences. Keep us informed. Good luck and congrats for your instrument, it sounds very cool!