My ultimate goal is to have an autocompleting list that displays all open tabs (in Firefox), which I can reduce to the tab I want to switch to next.
I can do the completion / combobox etc, but I don't know how to get the list of all names (and favicons wold be a huge bonus). Would be grateful for any pointers.
Doesn't GreaseMonkey run in the context of a single web page? I don't think it can access the other tabs.
If you make a normal extension, you can call window.getBrowser().browsers as is described here:
Detecting tab closed (after closed) from firefox extension
Aside from learning a little XUL, your extension might be easy to port.
How to build a FireFox Extension
If you just want the functionality, here's an add-on that does what you want already
https://addons.mozilla.org/en-us/firefox/addon/list-all-tabs-menu/