That's one frustration I have with Tmux. I want mouse scrollback, but don't want the other mouse controls. If I remember correctly I would accidentally go into copy-mode when I click-dragged my mouse by accident.
What I really want us an intelligent terminal, which attaches programming output to the program which produced it, let's me fold up long outputs, easily escape a long running program and store it output in a buffer for later checking, etc. But that seems annoyingly impossible.