Nice, you are putting your whole house on an UPS..
The problem I see with your method, is the UPS's inverter is connected to the GTI inverter.
In my experiment, my GTI was connected to a PSW inverter (like your UPS inverter)
and when the load was too light, the AC voltage from the GTI, climbed very high.
Soon, smoke was coming from my new PSW inverter..
If seems like my Chinese 1200w GTI can't use another inverter as a load.
It really needs the grid to allow it to work correctly.
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If I was going to use a GTI without putting any of my power on the grid,
I would use a current sensor to measure the power being used by my main loads.
That would be my two Sanyo heat pump/AC systems.
If the heat pumps were using more than 450 watts,
I could connect a 400 watt GTI to the house grid.
At that time, the grid would be supplying 50w and my GTI would be
supplying the heat pumps with 400 watts. No power lost to the grid..
When heat pump power dropped lower than 450w, the current sensor would quickly turn off the GTI.
Easy to do, with a small amount of extra hardware.
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One of the posters here did make use of an UPS, but he was using his solar
panels to charge up the UPS's battery. He replaced the small UPS batteries with larger AH batteries.
I think that system would be good to use with this PC, since it's on so much!
Cheers,
Rich