I use a backtick, but don't edit much e.g. markdown in my tmux sessions, and always use $(...) for command substitution so I don't normally feel any pain. One oddity with tmux is that to escape the control character you don't press it twice, you press the escape char then ctrl-b, so that is a lot of extra movement around the keyboard
Could you bind prefix + ` to insert a literal backtick? I've only ever used the default ctrl-b prefix so I'm not sure.
Backtick is my favorite too. Interestingly I thought it was an obscure choice, but it seems to be the 3rd most popular prefix from an analysis of tmux.conf files on github (after Ctrl+A and Ctrl+Space). I use `` (double-backtick) to escape the backtick and it's eminently reasonable.
I like ^Z, since it's about the only keybinding that's not used by common terminal software. To actually send a program to sleep, just double up: ^Z^Z
# In ~/.tmux.conf Change prefix key to Ctrl+z
unbind C-b
set -g prefix C-z
Control-Space is perfect for me
And compliments vim really well if you set your leader key to space.