Pressing ^A then a in screen should deliver a single ^A to emacs.

People rebind it. I bind it to ^o.

  # put this in your .screenrc
  escape ^Oo

I always rebind it to ^z. Since I never need to put a process in the background (I just open a new screen instead) when running screen, it never bothers me that that combo is a bit harder to type.

or if you never use toggle-input-method, maybe C-\

  escape ^\\

I don't use CONTROL-A to go to the start of the line, instead I hit ESCAPE 0

It works because I have my shell configured to use vi mode for command line editing.

i use the ratpoison window manager (it works a lot like tmux/screen, but for x11) and have control+a set as its prefix key. i use tmux for some long-lasting remote sessions, so to send a control+a to the shell running under tmux, under ratpoison, i type control+a, a, control+a, a. yes, i do it a lot. no, i'm not going to change it.

I actually only learned that ctrl-A works in bash 3-4 months ago, and haven't yet picked a new screen/tmux escape and retrained to it. Mainly because these days, I only use screen when I WFH or am traveling, when I ssh into my workstation. Almost nobody has ssh rights to a production machine, so I'm actually struggling to think when I would use it from my workstation.