I have plenty of access to shell accounts. But using a shell account to screen to another host just adds another layer of complexity, because when I lose my wi-fi connectivity for 1 second, then my SSH session to the shell account is lost instead of access to the real host. It still requires a waste of time logging into the shell account.
I think you may be constraining the solution down into impossibility. When you lose the network, you will lose the SSH sessions. Period. TCP will guarantee that. (Although not at "one second".) That's part of TCP's point.
The best you can hope for is either to set some stuff up as described so SSH automatically relogins to a screen session, or find a better network connection. Fundamentally, you can't patch around a bad network connection.
