Has anyone done this on the cheap? I've gotten a few quotes with a payback period of 8-12 years, which isn't great.

Yeah, I bought an inverter from eBay, and a battery from AliExpress. Also signed up to axle energy to reduce payback period. Most people would need an electrician to connect it though. If you just asked an electrician for a new circuit with a simple route to an isolator, it wouldn't be expensive.