Lot of good ideas here, but I would start with $20. I use the trick in my system for exactly this purpose.
Buy a cheap component to act as a filter to attenuate high frequencies, known to techies as a low pass filter. Fortunately, these are readily available as plug and play components, if you know where to look.
What you have to do is pervert a cheap signal isolation transformer, which is cheap because it rolls off the high frequencies, to use as a filter. You want it precisely because of this "defect", which would be a problem in many systems - but that’s the whole point in yours. The fact that it also works to isolate ground faults is just a bonus. I use really cheap transformers ($20 for a stereo pair - the ones I use are called 1st Source GL-100 Ground Loop Isolator - and - heresy alert - it’s for car audio) to tame the brightness of my digital front end (and no, it's not a cheap one). They come with RCA connectors, so they just insert between components, with or without interconnect.
You can daisy chain them for added effect.
Cables are another very good way to tune a system. What tends to cost money in cabling is good transmission of the treble information, which is exactly what you don’t want. So cheaper is probably more effective IN YOUR SYSTEM.
What you want, for your system, are high capacitance cables (thin coax) for interconnect, and low capacitance well-separated conductors for the speakers. That specification comes directly from Maxwell’s Equations - it’s physics, not opinion. Cheaper is probably better IN YOUR SYSTEM.
You might also try some carpeting or fabric wall hangings. I use two Persian carpets on the walls - decorative and effective.
Finally, you may be hearing the electronics. One possibility is the nasty brightness of cheap capacitors in the signal path, especially electrolytics, especially if they have been subjected to a hot environment. That requires surgery on your components, but is well worth it. I have no stock electronics anywhere in my system, other than the cartridge. But that’s a more extreme solution. Try the cheap tricks first.