You could setup a system with a larger lead acid deep cycle battery but I suspect a 1500w UPS would work fine. Buy one and test it! Five minutes before the generator kicks in makes me think this would work fine.
I had a Old APC smart UPS 1500 which is 1000w with 40ah batteries and it worked but was freaking out.
Yeah, that was probably exceeding the limit of what the UPS could do.
When I spec a system, I always follow the 80% rule. You want your load to be no more than 80% of capacity. In this case your load is (appx, according to the spec) 1090W, which means you'd want to rate for at least 1362W. A 1500W unit should work ok, but you're going to need to keep up on maintenance and batteries.
It's not going to be cheap, you probably want one with true sine capability and under/over protection. You're looking into commercial units at this point, not necessarily consumer.
Something I wanted to mention: A lot of UPS units rate their output in VA, or Volt-Amps which is exactly what it says, volts * amps. Make sure that you're getting something rated 1500W, not 1500VA.
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