There is a process running that occasionally accesses a port that I've tunneled through an SSH connection. These messages can be really obtrusive at times, so I am looking for a way to disable them.
11 Answer
Did you try the ssh -E option and redirect debug logs towards /dev/null ?
ssh -E /dev/null <server> Extract from man ssh:
-E log_file Append debug logs to log_file instead of standard error. 
