@dt42o First and foremost, all of my machines run on Linux, so if yours don't, I don't know how helpful my setup may be for you.
In short, my Pi 4 runs on the official RetroPie image, while the other two use the Ubuntu variants Kubuntu and KDE Neon with RetroPie installed like it's described here. I keep their rom directories synced with the tool Unison which is also available for Windows, but may have to be compiled from source. Many Linux variants have its binary in their software repositories, but I don't know if or where you can get a pre-built binary for Windows.
Conceptually, my PC keeps the main RetroPie setup where I do all scraping, testing and rom management. The other two only receive the end results and transfer any changes, saved games, hiscores etc. back to the PC, which in turn propagates them to the other "child".
I didn't automate this process fully, but use the GUI version of Unison manually, so my approach needs a sufficient amount of consequence in transferring any changes in a timely manner. Since Unison ultimately is a command line tool, automation should be relatively easy, but I like to have the full control and the "last say" in any synchronisation. 🧐