BTW, the output of a balanced power conditioner is not dissimilar from the 220V outlets your big appliances (range, dryer, HVAC, etc.) use.
It’s still not one +120 and one -120 V line. It’s two lines from the same transformer winding that run in opposite polarity. It is impossible to measure +120VAC. You can’t tell one from the other. The only thing you can do is measure the delta between them, which in this case would be 220VAC.
I’ve often wondered, along the same lines if the ideal situation wasn’t actually to run 220VAC to an audio room and use a combined step down and balanced output conditioner. Balanced power to balanced power essentially.
While I don't want to encourage anyone to poke around in a 220V outlet, I really don't! I can say categorically that if you took the most advanced multimeter on earth to your dryer's 4 prong outlet you can identify 2 hot lines, but cannot identify one as being + and the other - based on the meter's readings. Impossible. You could at best identify 2 lines which are either ground or neutral, and 2 lines which are energized.