lzr1621,
Most of the things called UPS - Uninterruptible Power Supplies - are actually fast-changeover SPS - Standby Power Supplies - especially in the lower ratings range.
They feed through the AC line supply until a low line voltage is detected, then turn on an inverter and switch it to feed the load in anywhere from 4 ms to 20 ms or so.
As you've noted, inverter output could be anything from 50% duty cycle square wave to a modified "stepped" square to a quasi-sinewave (usually a PWM waveform)... and cost goes from cheap to expensive in this progression.
Full-conversion (online) UPS don't have this switchover mechanism, and the load is always fed from the inverter (which may have any of the above waveforms, as well as fairly pure sine). I haven't seen one in a while, but fondly remember an early-80's vintage Sola 3KVA unit used to keep up our IBM 3270 communication controller - built like a tank, and just about as heavy
My guess is pure sinewave UPS aren't available in smaller sizes, and probably start in the 700VA/1KVA range (at $400-$500 and up).
If you already have an APC ES350 to experiment with you could hook it up, and see if the control system operates properly, and whether the transformer and/or solenoid coils tend to overheat when fed from it's output. At only 20VA load you might get on the order of 45 minutes of operation using it's battery.
OperaHouse makes a valid point - these smaller "brick" SPS are rated pretty close to thermal design limits, and aren't expected to operate for much longer than the OEM's recommended battery would keep it running (although, if only using 20 VA you might have enough headroom).
This SLA battery is rated for about 13.6 to 13.8 VDC float charge, and 14.6 to 14.9 VDC cycle charging, so I'd expect to see a regular lead-antimony battery (which usually runs in the 12.6 to 13.4 VDC float range, and 13.8 to 14.1 VDC cycle charging range) doing just about what danw2 observed - going through a lot of water due to the high charge rate.
A couple of years ago the battery in my Saturn started to go, and I measured 14.5 VDC when charging. Thought this was high, but learned it is normal for calcium alloyed plates in the Delco Freedom series batteries.
I'm thinking this would fit better with the UPS battery charger's output, but I've read that batteries using calcium plate technology are particularly unforgiving of deep discharge cycle operation - so probably not a solution you'd want to put money into.
Idle thought - does anything
need to be powered from 120 VAC or 24 VAC (such as a proved flame controller)? Was thinking one way to do this is change from 24 VAC coils to 12 VDC coils, and power everything from a deep cycle 12V battery with a float charger across it. Con - you'd need to roll your own low battery voltage interlock circuit ...