Idk, what's the torroid next to the relay?

If it's the same part (red-wired donut held to board with hot glue) that's on my DE Simpsons, it's an "inductor", whatever that is:
https://pinside.com/pinball/forum/topic/fs-data-east-simpsons-300-seaford-long-island-ny#post-1728911

A toroid is a type of Inductor.
I was pointing out that I'd suspect anything near that Inductor or maybe it and of itself.
Given you've already indicated it's a LAMP filter... it seems plausible that toroid is part of the problem.

I don't think there is anything "WRONG" with these components; only that their proximity is suspect. And given the problems we all have with feedback/hum... it's likely a design defect.
Given the "filter" is louder; it could be that the filter is causing feedback into a near by circuit.
The question is … do any of the audio circuits / power supplies have proximity near this toroid?

I hope you figure it out. The noise drives me crazy.

The toroid could be introducing induced current into any of the audio circuits.
That said; a quick proximity check indicated to me that the two parts of the circuit are pretty isolated... at least from an MPU board perspective.
I think the toroid is just a symptom of the larger problem... IE the current flowing into the switched lamp drivers is massive and is just loading the transformer in general which leads to "the singing" being represented throughout the system including the sensitive audio circuits.

I'd be happy to be wrong tho.

I just played some games on mine … I don't have the buzz... well nothing I can hear of the fan anyway.
If I had the buzz; I was going to pull the board and look at the Ceramic caps on the output of the 3 output amps (MB3730 U31-U33).

Those should really be polypropylene caps:
http://aeaaudio.com/audiophile-quality-capacitors-going-beyond-the-simple-re-cap/
and
Mr Carlson's Capacitor video.

I'm betting those caps in the audio section are ceramics... and if so; Mr Carlson sums it up quite nicely:

I wonder out loud if fan vibration is some how causing those ceramic caps to sing. Doubt it; but it'd be an interesting experiment.

At this point; I'm more inclined to believe the +12V circuit is to blame. It'd be real interesting to see a capture of the "hum" as it compares to the 12V supply at CN2-6 on an oscope.

It's also be interesting to see if the hum is coming from one specific speaker.

Dest has a backboard fan at one of the vent holes on top.

Sorry to bring back an old thread, but my BTTF used to make the same loud buzzing sound during attract mode. I just replaced all the stock speakers with Flipper Fidelity and the buzzing is much much much lower. Doesn’t even bother me anymore, but YMMV. So while it doesn’t solve the problem completely, it helps remedy it. Plus the added bonus of better quality audio.

Tarnished grounding points on the backs of the circuit boards can contribute to the buzz. I had bad GI buzz on my Rollercoaster Tycoon. I had to remove the main board to do a little work. Before I put it back I cleaned up the mounting posts and the ground contact pads (the flat area of solder that touches the mounting posts when you screw the board to the game). The buzz has all but disappeared.