Not an RStudio programmer & this isn't an RStudio solution, more of a way to reduce the irritation, but have you looked into keyboard shortcuts for assigning windows/programs to monitors? I have a few such things (in Linux, so chances are this doesn't apply to you) and it's made multimon organisation so much easier. Presumably you know you can pop out tabs to independent windows using the little icon near 'source on save'? The tab names bug has been patched & will be in the next Preview version, hopefully soon.
Back on shortcuts, it might even be possible to assign specifically named windows (e.g. "Console") to monitors or workspaces via your OS or a 3rd party multimon program.