Macros in GNU screen?

You could also arrange some files this way:

~/.myscreenmacro:

split
focus down
screen

~/.screenrc:

bind e source $HOME/.myscreenmacro

This is a little clearer than the other ways.

Have you tried:

register s ^aS^i^ac
bindkey ^a,, process s

From the depths of the screen manual:

register [-e encoding] key string

Save the specified string to the register key. The encoding of the string can be specified via the -e option. See also the "paste" command.

and:

process [key]

Stuff the contents of the specified register into screen's input queue. If no argument is given you are prompted for a register name. The text is parsed as if it had been typed in from the user's keyboard. This command can be used to bind multiple actions to a single key.

Screen's command eval is handy for creating this kind of macros:

screen -X bind e eval split 'focus down' screen

Commands expecting arguments (like focus down) need to be quoted (single or double).