SOLVED
Problem: When my UPS does the switch-over from line power loss, the pellet stove runs but you can hear the stove motors slow down, and the wattage meter on the UPS drops from ~150w nominal to ~100w nominal. I say "nominal" because the auger is running every few seconds and adds ~25w to the load.
Setup: I have a pellet stove to heat my house, it draws at most 450w on 120vac. However once it's running good usually consumes ~175w.
I got a 1300w Uninterruptible Power Supply used on eBay, an APC BR1300G. This unit should be able to power over 1000w(rated at 1300w) easily and do it for days given you have enough battery backup. It uses 24vdc for backup power. It came without batteries-- I hooked up two group 31 marine deep cycle car batteries in series to provide this power, and the UPS is charging correctly. The DC wires are crimped tight, only draw about 15A 24vdc at this load, and do not get warm.
Edit to answer some questions: I'm not asking this UPS to turn on the motors from stopped, I'm only asking it to keep them running at a tiny wattage requirement. I get that start-up current is much more than running current.
Line voltage is between 118v and 120vac depending on the day. Output voltage on backup power is 118-119vac, according to the UPS screen. (This, however is incorrect as I just found out. 55v!) Hertz is 60 from line and 60 from backup power. I don't know what you mean by "measured the affects of the motors", nor do I know what high phase angle loads are.
Battery wires are 12ga, and the longest is about 2.5ft long. Which is just fine for less than 20A sustained load @24vdc.
"You are expecting a used device with external batteries meant to drive computers with a pseudo sine wave to drive motors perfectly. That seems unrealistic to me. – StainlessSteelRat" I'm expecting a 120vac appliance to run on 120vac provided by a device designed to power stuff with 120vac. If there's a bunch of flavors of AC and they are not all compatible with each other then this is where I get to learn about it. Believe me, if I could have found this answer by googling it I wouldn't be here. But I couldn't. Now that I know motors are somehow special maybe I could search using different criteria.
A big thank you to Tim Wescott for you answer!
I probed the UPS output on line power: 120v. Probed it on backup power: 55v!!! Turns out this was wrong, I measured the voltage wrong and figured it out later when my sine wave UPS arrived. It was putting out around 120v. But the stepped sine wave was totally messing with the motors and were drawing 15A @24v for a 100w load...bad stuff. My sine wave UPS now takes over using only 6-7A @24v.
The above reading was taken with a True RMS multimeter, which according to APS is the only way to get an accurate reading of the stepped-sine wave output when running on battery power.
Link: https://www.apc.com/us/en/faqs/FA157483/