The ground-neutral voltage is no big deal. You ought to have some voltage difference if there's any load on the circuit.

If the panel filter does nothing, That suggests the noise source is there in the barn, but I suspected that anyway.

I would suggest turning off each electrical load in the barn, one at a time, and see if the noise goes away.

I suspect the fluorescent lights.

In the common 4’ fluorescent lights, it's fairly easy to change ballasts. The cheapie electronic ballasts can be quite noisy. To a certain extent, ballasts are noisy by nature, but they can function on audible (2k) or inaudible (50KHz) range dependong on design. GE makes ballasts of superlative quality for about 30% over their top tier competitors. If the lights are the issue, try one and see if that corrects it.

Another option is to go LED, but they too have switching power supplies so beware of quality issues.

The ground-neutral voltage is no big deal. You ought to have some voltage difference if there's any load on the circuit.

I would start by eliminating radio jamming. Get a battery powered, portable radio - a car or truck will suffice. Do you get the same interference? If so, the problem is radio (RFI). AC power line conditioning will do nothing. Most likely it's duff ballasts, I would be curious about the brand of ballast. Otherwise...

If the panel filter does nothing, that suggests the fox is in with the chickens, i.e. on the same side of the filter. If possible, move the filter so the lights and stereo are on opposite sides of the filter.

To a certain extent, fluorescent ballasts are noisy by nature since they are driving a high frequency signal (2k-50kHz) to the unshielded lampholders and bulbs. But they may also make unnecessary RFI or line noise. GE makes ballasts of superlative quality for about 30% over their top tier competitors. If the lights are the issue, try one and see if that corrects it.

Another option is to go LED, but they too have switching power supplies so beware of quality issues. They are inherently DC and do not radiate high frequency AC anywhere beyond their power supply circuit, which is easily shielded if the manufacturer chooses to.