Gee, I don't want to pour cold water on this, but up above there somewhere you said you wanted to replace the batteries in the ups with marine batteries. Don't do that! The problem will be when the power does fail and the big batteries get run down somewhat. They will start to charge when power returns only the ups won't be able to supply enough power to feed those big marine batteries and it will fail.
These ups units are fairly cheap these days because of the computer market--we all need them to keep the PC's from crashing every time the lights flicker. Demand has brought the price down, but it also has made the designs for the units very efficient to keep the costs down. Read that as just enough guts inside to charge the batteries they come with, no more.
I work in a place where we use hundreds of 1000 to 2000 watt ups units. They fail all the time. We use various brands, different batteries, etc. After a power outage, the electrical load on the protected circuits is about double the normal load due to all the batteries charging. This is when all our ups units fail--during the charge cycle from too much demand from the suddenly heavy load of a dead battery plus the normal load from the protected circuit.
If you need longer run time from your ups for the coal burner, get a bigger ups and maybe then you can park it up by the stove and avoid the wire going from upstairs to downstairs.