Your script, as in your example, will get executed by your sell, not the one in the screen. You need to tell the running screen to read a file and execute it - that's what the -X option is for.
Try
tempfile=$(mktemp)
cat > $tempfile <<EOF
cd ~/servers/StarMade/
sh StarMade-dedicated-server-linux.sh
EOF
screen -X readbuf $tempfile
screen -X paste .
rm -f $tempfile
You can leave screen running in a 2nd terminal session to see what happens.