iceweasel is just another name for firefox, so that will have the same problem with kompozer, I think.

For hacking kompozer's mozilla-run.sh you would of course need some basic knowledge of shell scripts. But you could just give it a try and open that in an editor, have a look whether a specific browser is called therein, and replace it by /usr/bin/epiphany-gecko. But also epiphany is based on Mozilla, so I wouldn't give it too much hope.