I use a complex system for screen. My default escape is set to \140\140, which is backtick. The Ctrl-A complicates both Emacs and command line editing for me within Zsh, and I dislike Ctrl-O (2 hand operations for most screen actions).
I rebind 's' to screen 1 so that new sessions are created from left to right on the keyboard starting at 1. This allows me to reserve screen 0 for what I consider persistent or reference windows. It's very quick one handed gesture to (backtick)1, (backtick)2, (backtick)3 to swap between windows.
The issue with using backtick in a Unix environment is when attempting to cut-and-paste shell/Perl script code. For this reason I bindkey F11/F12 to switch between my escape character.
bindkey -d -k F1 escape ^O^O # bound to F11
bindkey -d -k F2 escape \140\140 # bound to F12
This will swap the escape to Ctrl-O for when I'm doing cut-and-paste operations. I've found hitting a double tick is simple, and a good trade off for most screen operations.
Revisiting this answer with a newer solution that allows for toggling the mode by hitting F12, and using a caption to indicate mode.
## command characters
escape \140\140 # default is `
## sets caption and escape toggle
bindkey -d -k F2 process a # bound to F12
## initial caption
caption always '%{= kW}%?%F%{+b KW}%:%{= kK}%? %= %?%F%{-b .c}>>>%{-}%? | %-w%{mW}%n* %t%? @%u%?%{-}%+w '
## registers to toggle bindkeys
register a "\140:eval 'bindkey -d -k F2 process b' 'process c' 'escape \\017\\017'^M"
register b "\017:eval 'bindkey -d -k F2 process a' 'process d' 'escape \\140\\140'^M"
## registers to change captions
register c "\140:caption string '%{= kW}%?%F%{+b mW}%:%{= kK}%? %= %?%F%{.c}ALT%{-}%? | %-w%{KW}%n* %t%? @%u%?%{-}%+w '^M"
register d "\017:caption string '%{= kW}%?%F%{+b KW}%:%{= kK}%? %= %?%F%{.c}>>>%{-}%? | %-w%{mW}%n* %t%? @%u%?%{-}%+w '^M"
~/.tmux.conf
don't forget to restart tmux server for changes to take effect (superuser.com/q/188491/105108).