wrote

This simple system could be put together for under $300. Any thoughts
on how it might work?

Sounds like you are on the right track. One thing I would think about
adding, is a way to automatically correct for the rate gyro's drift.
Perhaps a static port out on each wingtip, and a differential pressure
comparison? It could just do a correction based on a timer every few
minutes, perhaps.
--
Jim in NC