Can I rebind Screen's escape combination to something else?

The C-a combination can be remapped from the .screenrc file, with the bind command.

This website should be a huge help to you: http://www.softpanorama.org/Utilities/Screen/screenrc_examples.shtml

From my own .screenrc :

# replace Ctrl-A with Ctrl-O
escape ^Oo

From screen's man page related to the -e option:

       -e xy
            specifies the command character to be x and the character generat-
            ing a literal command character to y (when typed after the command
            character).   The default is "C-a" and `a', which can be specified
            as "-e^Aa".  When creating a screen session, this option sets  the
            default  command character. In a multiuser session all users added
            will start off with this command character. But when attaching  to
            an  already  running session, this option changes only the command
            character of the attaching user.  This  option  is  equivalent  to
            either the commands "defescape" or "escape" respectively.