... what I want is a "true sine wave" UPS. As I understand it, this means that you're always running off the battery with corrected voltage available even during brown-outs, surges and spikes.
Apples and oranges mixed alert.
A "true sine wave UPS" outputs, well, a true sine wave, as opposed to a stepped sine wave, or square waves.
A UPS that "always running off the battery with corrected voltage available even during brown-outs, surges and spikes" is an "online" UPS, "always online", or a "dual conversion", or something similar. UPSs that are not "online" normally provide power directly from the mains, only switching to the inverter if the mains fails.
You can have any combination of online and standby, and true sine versus stepped.
As others have noted, if you're protecting digital electronics, it'll have a switched mode power supply, and wont care what the input waveform looks like, even DC is acceptable to most SMPSs. If one is using stepped output UPS and there is noise appearing in the audio, then there is another problem present.