Your use of p surprises me if you don't use b for emacs reasons! How do you go up a line!?

Iam pretty sure that was a recommendation in the emacswiki to use ^P instead of ^A as prefix key (that must be 15+ years ago). I think I didnt invest to much energy to think about an alternative. I almost never use ^P in my terminal emulator, but I use ^A all the time.

I usually never do heavy editing in a tmux window. Rarely I use emacs in a terminal window these days. I use tramp to remote connect and edit comfortably in my X session.