An easy way to cheat this in order to save the most money is to buy a UPS with high pass-through power. On older models a typical pass-through limit was 1440w, which is well above what a P2S would draw even in peak. That will let it sail through the initial peak power demand. Steady state power draw on a P2S is in the range of just 100-250w, so aim for a UPS that can sustain, say, 300w+ continuous in UPS mode.
All you’re giving up in exchange for substantial monetary savings is 1. you can’t start a print during a blackout that’s already in progress, and 2. if a blackout were to occur during the initial heatup phase, the UPS would overload and shut-off, which would prevent your print from starting. i.e. you’re not giving up much. In neither case would you lose a print which is already in progress, which is probably what matters most to you anyway.