Some good comments above from some quite knowledgeable folks - nice to see and is why I like to frequent this forum. I agree that adding a couple of dedicated 20A circuits with 10-12 AWG wire should do it _ IF the in-wall wiring back to the breaker is the problem. The only unaddressed point (as of when I started typing) came in the OP's second post where he specifically comments on the lights dimming. (…the light dimming issue, IS happening…)
More info on how this manifests itself might help us help the OP. If lights dim, something is not up to snuff somewhere. Are they in the same room and on the same circuit? If so, then that narrows things down a lot. If dimming happens elsewhere in the house and NOT on the same circuit, then I would IMMEDIATELY ask an electrician or the utility company to check the service entrance feed to the building. Some utilities won't check past the meter so you may need the electrician for a "last mile" check between the meter and your breaker box. A non-direct analogy - I once moved into a building and found one leg that fed my stove was leaning against its connecting lug - not clamped at all. Truly scary. Not every installer is working at 100% all the time. There may be a loose connection at one of your outlets or anywhere back to the breaker box or even the pad mount or pole.
Terminology / grammar check: You have a SERIES of outlets connected in PARALLEL along the circuit, so each gets the full voltage. At some point back-wiring came into vogue to speed installation. That enabled installers to just poke the wires into holes in the back of the receptacle. No loops around screws that need to get tightened just right. Fast and easy, but not nearly as good a connection and then the receptacle essentially becomes a buss bar and IS in series with the other outlets, but each plug-in point is still in parallel with all the others.
Another take on the series / parallel issue: A good wiring job with large wall boxes and lots of space will have the wires going to the breaker box come to a 3-way connection, with the lead to the next box under the wire nut as well as a short pigtail to the receptacle in the box. This way the receptacle is never in Series with the other devices down the line and the inevitable movement from thermal expansion and years of plugging and unplugging devices has less impact on the connection at each device, and half as many connection points to loosen over time or be suboptimal initially.
15A breaker and 15A outlet circuit? Some guys may have cut a corner and only used 14 AWG light fixture wire instead of the 12 recomm for outlets, esp since the push-in receptacle back wiring connection holes are not supposed to accept 12 gauge and it is so much quicker, easier and cheaper to just cram the smaller 14 AWG in a hole. You can also get a lot more voltage droop that way.
Back to the HT room. How / when does the light flicker manifest itself? During a major but quick explosion, an extended pass of a tank rumbling past you, Aircraft takeoff or extended pipe organ bass note? A long rumble will deplete much of the stored power in most amp power supply capacitors. Transients are easy, but extended high ampere power response sucks once the caps go flat. If things blink on even a loud, but SHORT rumble, then maybe a PSU capacitor is no longer up to snuff. Seek it out. Lots of how-to info elsewhere. I would rotate through my amps and see if I can narrow down my search first. If basic fixtures and wiring were both up to snuff, then the lights should not follow the music. Upgrading to Audiophile outlets, in-room cables, etc. can be done later if you want as frosting on your cake!