I have a bunch of servers, on which I run experiments using screen. The procedure is the following :
ssh to server XXX
So you're using screen to keep the experiments running in the background, or what? If so, why not just start it in the background?
./experiment &
And if you're asking how to get notification the job i done, how about stringing the experiment together with a mail command?
./experiment && echo "the deed is done" | mail youruser@yourlocalworkstation -s "job on server $HOSTNAME is done"