I followed (one of) Ben Heck's instructions on getting composite video out, but while everything checks out circuit-wise, and I get some video output, it was dirty and I couldn't stabilize it. Not a surprise since it wasn't working well to begin with!
Flashback 2 from a few years ago, it turns out there's a way to add a cartridge port to it for playing old games. Instead of using the Flashback to make something even smaller, I wonder about going the other way: transplanting the Flashback 2 into the original 4-switch VCS, using as much original hardware as possible. It doesn't look like anybody has gone in this direction, but thankfully the VCS is well documented online; even the original service manual in PDF. "Atari Hackback" seems like an appropriate project name. Thanks to Craigslist, it took a day to find a clean Flashback 2, and this handy reference shows where the cartridge pins go. There are a LOT of signals to reroute, but I'd like to preserve the hardware's connection to the PCB, so will need to find other solder points for attaching leads.