Continue what you’re doing on the desktop and set up beeper with only your Facebook account to handle messages from your phone. It’s still not great, but I think it’s the best you’re going to get. You’re really only gaining Facebook, not seeing where you’re connecting from. Also, Beeper is just a pretty front end to a matrix server with a bridge connecting to Facebook Messenger. You could totally run it yourself if you wanted; check out the “self-host” link near the bottom of the page.