Synchronize VS Code Keyboard Shortcuts between Windows and Unix

VS Code has a "Settings Sync" feature to synchronize settings between different installations. However, it does not sync Keyboard Shortcuts across platforms. I want the same Keyboard Shortcuts for both Unix and Windows, and I want it to automatically update all installations when I make a change anywhere. I've manually copied keybindings.json but don't want to do it every time I make a change. I have not found a 3rd party extension that works. Thanks for any help!