Thanks for the advice, guys.
I ended up going with a Raspberry Pi. If this cab had any original hardware inside of it at all, I probably would have attempted to salvage it and keep everything original.
I spent several hours screwing with the Raspbian distribution to get it perfect. There were issues that needed to be resolved from hissing audio to inadequate screen resolution. When I turn on my Galaga machine now, I now get a black screen for a few seconds and then Galaga starts without any Linux text or Raspberry Pi logo ever showing up on the screen.
This probably cost me more money in time and effort than buying a 35 year old Galaga board... but my goal here was reliability. I'd be happy to share my Raspbian image if there is any interest. The only noticeable difference between a real Galaga machine and this one is that the screen is black for a few seconds longer when you first turn it on. That is a reasonable trade-off for my purposes.
Edited by Brad O. (06/10/15 04:32 PM)