My take on this (similar to others):
You should only do this on a pure sine wave inverter, modified sine is a gamble, you don't know what's going to fail. I had an air purifier that lasted being turned on a single time on modified sine, and any kind of voltage conversion equipment is also likely to be strange. I got to the point that I would charge power tool batteries on modified sine, but that's about it, and I think older tool battery chargers had bigger issues with it (hearsay).
Your UPS will not clean up dirty power unless it's a very expensive UPS in "in-line mode" or similar. Normal cheap UPS just pass the power through when being provided with power on their input.
And yeah, the person who pointed out you shouldn't be exceeding the UPS rating is definitely correct.
Nice thing? When you move your loads back from inverter to grid, they don't have to lose power for that cutover.