When not using tmux/screen, the complete invocation is C-a a M-x roll-eyes RET Backspace.

This is really easy to remedy: just bind send-prefix to C-a C-a. That way you'll be able to easily go to line beginning inside tmux, and outside you won't type the unnecessary 'a' character.

Moreover, I forgot if it's the default or if I set it somehow, but in Emacs a single C-a goes back to the beginning of a line, but C-a C-a goes back to the beginning of text on the line, which is almost always what I want anyway. So I press C-a twice anyway, everywhere, and I don't have the problem you described at all :)

content of dot screenrc file:

defbce on

defutf8 on

escape ^]^]

markkeys "h=^B:l=^F:$=^E"

setenv LANG en_US.UTF-8

startup_message off

term $TERM

Copy pasted from somewhere, i do not recall from where.

ctrl-A is now ctrl-]

This does not clashes with Emacs, ctrl-A