So, I replaced all my UPSes with LiFePO4 batteries supplied by Victron AC->12V chargers. Routed the battery contacts directly to all devices that consume 12V (WiFi AP, network hubs, SLA 3d printers). Used 12V -> 5V adapters to supply 5V / USB2 devices (R-Pi servers). For 19V, Drok DC-DC boost converters work great.
Result: threw away 3 UPSes (different APC models). Overall power consumption with AC present dropped by about 40%. Time on batteries (same Wh battery capacity) increased by a factor of about 20 (yes, 20 times: that's not a typo). Evidently, AC waveform generation is extremely power-hungry