Redirect Output from remote connection using a heredoc

maestrojed.bash

#!/usr/bin/env bash

# sets some vars so the editor doesn't report errors
deployID="1234" # A custom ID retrived in our script, for demo, hardcard
logFile=$(date +%b-%d-%Y-%H-%M-%S)-$deployID".log"
projectPath=${PWD}
sshUser="maestrojed"
sshHost="maestrojed.example.com"

set -x

# redirect all output to the log, while still being verbose on the screen
exec > >(tee -i "$projectPath/deployments/logs/$logFile")

# do some stuff, a shortened example for this demo
cd temp
ls

# Now runs some commands on an SSH connection using a heredoc. 
# I also want to redirect the output of these commands, run on the remote server, to my log file. So I capture it in a var $serverOutput
ssh -tt $sshUser@$sshHost <<EOF
pwd
ls
cd myDir/
ls
exit
EOF