Then I think a 12v low amp light bulb (automotive) will be cheaper/easier and more suitable.. Anything up from 12v will cause issues and the standby on the inverter is clearly more than I had counted on....
They make 12 volt and 24 volt heat tape at 3 watt and 5 watt /foot. I looked into it last year when my pipes froze on my remote property. Haven't bought any or installed it because I'm not there much (yet). The 120 volt heat tape is much cheaper and I'm pretty sure they make it in 240 volt also. Just search around. It's also called heat trace.
Every man's dream ... to live in a small paid-for home, live off the land, off the grid, with two good-looking, willing fine women. Unfortunately it is not every woman's dream.