How to run a command inside screen such that you can get back to the command’s parent shell

You could start screen with the -L option. This will cause screen to create a file screenlog.n (the n part is numerical, starting with a zero) in the current working directory.

In your case this would look something like: screen -S session_name -L -X eval 'stuff "$cmd"\015'

As long as you remember to clean up afterwards, this should match what you are after.

For last line of the log, it can easily be obtained with tail -1 screenlog.0, or the entire log can be parsed however you wish.

I see two way to do this, the first one is to make a .screenrc file by host.
Like .screenrc_serverA, .screenrc_serverB, ...
In your shell startup script set SCREENRC to something like .screenrc_`hostname`
Of course you can use the source command of screen to include something like .screenrc_default in each custom .screenrc_… files so that they only contains a caption/hardstatus line and not the whole configuration each time.

The second way would be to execute commands like screen -X hardstatus lastline ... (using if tests to execute the command with different value for ... depending of the hostname) in your shell startup script. When you will log on the server, screen -X will do nothing because screen will not yet be launched, but each time you open a new windows in screen the hardstatus will be updated.

Of course the 1st solution is better because the second one will refresh the hardstatus line each time you opened a news windows which is probably useless as the hostname will not have changed.