To answer my own question:
Ignacio's answer takes care of the large icon on the system menu, and the taskbar launcher if you add one. Changing the icon on the taskbar button/panel button took more digging.
Uninstalling the 'native' Firefox from LMDE (`sudo apt-get remove firefox`) and installing the tar.gz from < still left me with the orange eyeball on the panel button.
So I started hunting through folders, and eventually found it: The icon I can't stand is in `/usr/share/icons/Mint-X/apps/16/firefox-png`.
I renamed the file to `firefox-ugly-icon.png`, and copied in the icon I want (from another system). Problem solved.