Victron data sheets publish their inverters are less than 3 percent THD. Same for Exeltech. Exeltech publishes they are closer to 1 8% under load. If you look around the off grid community, there are plenty of videos where people have a scope attached to their setup. Plenty of video show prople loading and overloading inverters. Usually with a bunch of space heaters A overloaded high frequency inverter sine wave looks highly distorted. But then again, I measured a branch wire at a home on utility power with 2 Shunyata Denali on the branch and the wire had 18%THD and was very distorted. Part of the reason I advocate multiple branch wires to the rack. Part of why 2 inverters and 2 batteries to 2 power strips would be a good way to feed a stereo.
Victron has a 20,000 switching FET that turns the DC to AC, then a large copper core step up transformer boosting the voltage for 24 to 120 volts. 20,000 is right in the sweet spot of a Puritan filter and I assume most any other filter. I don't see any reason you can't have a absolute distortion free 120 volt power supply at the rack.
A battert with a 100A DC fuse on the DC cable to inverter. A AC cable, less than 3 feet with a female plug from the inverter going into a filter with a CB or fused IEC inlet.
A single 100AH battery at 24 volts is 2400 watts. Run to 80% thats 1900 watts reaerve run time. Constant draw of 500 watts is a solid 3 hours. Add a secod battery its 6 hours. If you got desperate, turn the charger back on. Run indefinitely.
Inverter is about $1500. each. battery about $1400 each. Chargers $500 each. Cables about $500. Your done. Take it with you when you move.