Your icon theme (whatever you're using) is probably inheriting another theme which is inheriting another theme etc...until it finds all the icons. Look in your theme's index.theme file and see what icon theme it inherits. Look there for the battery icon. If you dont find it there, look at what theme that inherits..etc. You'll probably find the icon after 1 or two iterations.
you can find index.theme in /usr/share/icons/[theme name]/index.theme
The applet for the Battery Monitor plugin does not use a simple icon. It draws a 2D vector graphic using the Cairo library. You can only edit the panel item's appearance within the limits provided by the plugin, which does not currently include an option for replacing it with an icon.
It's normal that themes do not affect this panel item's appearance because, afaik, editing the package's source at lxpanel-<version>/plugins/batt/batt.c and installing your new custom version is the only way to make dramatic changes beyond what the plugin's settings currently allow for. Alternatively, you would have to find a different battery monitor plugin or write your own if you want to see any major changes here.
Editing Battery Monitor's Appearance Settings:
Editing the file ~/config/lxpanel/LXDE/panels/panel.config directly does not immediately update or refresh the appearance of the battery monitor panel item.
Instead, right-click the battery monitor applet and select "Battery Monitor" Settings (where you'll notice it's actually two ugly green rectangles). The plugin should apply the new configuration and update the display of the widget upon closing this window.
Using a Different Plugin:
Some plugins, such as the GNOME Power Manager, can be themed by use of static icon images. From the officieal GNOME Power Manager project site:
The notification icon can display a device in the tray. The icons can
be themed with custom icons for each theme, or fallback to a standard
default.
This should allow you to use your theme's icons. Install it with apt-get.
apt-get install gnome-power-manager
You may or may not need to manually add @gnome-power-manager to your /etc/xdg/lxsession/LXDE/autostart file. If you have any problems, please create a new question that pertains to Gnome Power Manager specifically.
Writing your own battery monitor plugin:
The details of writing your own plugin are beyond the scope of this question, but for those interested and willing to code a bit, see How to write plugins for LXPanel - LXDE.org and Debian - How to monitor battery capacity. As mentioned before, the battery monitor plugin included with the lxde-common package relies on the Cairo library. A good tutorial for working with that can be found at Cairo graphics tutorial.
The bounty requests: "Looking for an answer drawing from credible and/or official sources."
I am looking at the source for this plugin from lxpanel-0.7.1 downloaded at LXDE - Lightweight X Desktop Environment - Browse /LXPanel (desktop panel) at SourceForge.net
; it has what I call the "orange eyeball" icon. 
Best Answer
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 http://getfirefox.com 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.