That last part is the catch. Switch imediatly.
Now there are a couple ways to do it, but you would have to find some other way to calculate how long it would last.
I don't know if it would be any cheaper building it yourself like this, but here would be my list.
6 deep cycle marine batteries wired in paralelle.
A float charger with 6 slots.
A power inverter
Wire that all up with only the charger going to main power.
the stove would always run off the inverter and batteries. When main power cuts out it would stay with the batteries to run.
based on needing a 200 watt inverter, my guess is some where around 800 for all that.
2 problems I see, first,most inverters aren't rated for that, unless you get a generator type inverter.
second, the charger may not be able to keep up with the current draw when the stove is running.
but that is why apc gets the big bucks. The one they claim will work runs around 1100.