With the greatest of respect, the way you casually drop technical terms out of context suggests to me that you really don't understand how terminals work in the slightest. (That and the new revelation that you're restoring your BBS snapshots in random orders yet expecting your terminal to be smart enough to guess where to resume). This is why I think we are having such a high degree of difficulty agreeing on your problem.

The reason I commented about hacking the BBS software is because that's the only way to solve the weird requirements you're asking. You can complain about my suggestion all you like but it's your unusual requirements that are at fault The fault here, not my solution.

Maybe you need to stop and think for a moment that perhaps what you're asking is silly rather than just assuming that everyone else on the internet is stupid.

The closest work around you're going to get (and is buildable with your experience) would be to build a terminal server (like a minimal Linux distribution running on a VM or Raspberry Pi) which you can SSH onto from Linux or Windows (eg via PuTTY) and which has a serial interface to your BBS software (be that virtualized or physical). Install 'tmux' or 'screen' onto the terminal server and when you SSH onto the terminal server reattach to your screen session. That screen session will be connected to your BBS and you'll then have your detachable but persistent terminal sessions.

Edit: If your terminal server is a VM and the BBS software is a DOSbox instance running on the terminal server then you also only need to snapshot one host and have persistent scroll back PLUS the ability to restore from random snapshots. The only thing you would lose is your TCP/IP handshake to the xterm / PuTTY session but they're detachable anyway via tmux / screen so you'd just have to SSH back into the host and reattach to your multiplexer (screen / tmux).