Given that I have 'mission control/displays have separate spaces' unchecked: is there a way to swap spaces between displays (and assign a shortcut to it)?
For example: if I have 'Desktop 4' on the left monitor and 'Desktop 2' on the right monitor, I'd like to end up with 'Desktop 2' on left and 'Desktop 4' on the right.
If you have 'Displays have separate Spaces' unchecked, then you cannot do what you are looking for.
The 'Space' will automatically be the same Space on both monitors, you can't have one Space on the left & another on the right. You would need to re-check 'Displays have separate Spaces' in order to do that.
Then you could call up any Space on any monitor.
Because I don't use it that way myself (& refuse to mess up my careful setup yet again to test it ;) you'd have to test whether a given Space on the left has the same window contents as when you call that Space on the right. My guess is that they would have different contents, as it's possible to call the same Space on each, & for that to then be a mirror wouldn't make much sense.
So, I'm pretty certain that by either method, you cannot achieve what you need - which I am assuming is effectively to swap the contents of one screen for the contents of the other.
displays have separate spaces means, I was hoping to get the same set of spaces on both displays, but being able to switch them independently. Second, my research shows that apple closed all the APIs for working with spaces, so no kind of automation is possible.