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.
A client of mine pays for an SSL cert he doesn’t even use. I’ve told him before I moved him to Let’s Encrypt because I was able to automate the renew process. He decided he needed to continue paying for the SSL cert. I told him we are not using it, but he doesn’t believe me. So he continues to pay for it.