Use small UPS to power steam boiler

No.

You definitely want to put the humidifier on its own circuit, or a circuit that is not shared with two powder/bath rooms. You could look for a convenience receptacle in the basement and determine if it's on the same circuit. If not, you can probably come out of that for the humidifier. If the humidifier pulls it's full 7A rating when it starts, you probably want to avoid having it share a lighting circuit, as the lights could dim when it turns on. That can cause premature wear on ballasts and greatly reduce the life of any incandescent lamps you might have in use. Take care to know exactly what else is on any circuit you find in the neighborhood.

NEC requires wiring devices, such as the relays you're talking about to be listed and approved. Assembling something to cut the power to the UPS when the humidifier kicks in using all listed and approved parts does not constitute a listed and approved device. Your approach, while very creative gets a little too far into the "Rube Goldberg" brand of tinkering.

My advice is, have an electrician install a single use receptacle for the humidifier on its own 15A circuit, even if that's slightly overkill. If your panel will not accommodate this, and tandem breakers aren't a possibility, then consider increasing the size of your panel and / or service.

Two bathrooms on a single 15A circuit is problematic enough, it sounds like you need to bite the bullet and get a few additional circuits where they're needed.

I will give this a try.

Physics says that water can not make steam, at sea level pressure under 212 degrees F.

It is also why steam pipes and automobile systems are under pressure, you can hold more heat, when water is under pressure and not have it boil. Pressure cookers cook food faster for the same reason.

The only way to make steam, from water, at 180 F, is to do it under partial vacuum.

To get water to boil at 180 F, you need to reduce the air pressure to about 7.5 psi.

7.5 psi is a column of water about 15' tall.

If a boiler tank, had a 15' tall pipe, filled with water, and caught between a drain trap and the return to the boiler, it would make steam at 180 F.

I have a physics background, and I am not a stationary engineer, well not a train engineer either, to be honest.

Hopefully someone who has actually worked on a boiler system can take this and run with it.

• Note, never pay someone to work on a boiler that thinks the temperature of the water should be below the boiling point of water.

You are better off hiring a competent plumber to work on a storage water heater. You get the same result with fewer parts, faster, and for less money.