That's pretty cool, thanks for sharing that :)
I'm personally a fan of plugins that do one thing really well, instead of getting bloated by trying to do everything, so I try to only include features that most people will use. I haven't heard anyone asking about full-screen support, so it's not a likely candidate for being included in future releases.
At the same time, though, I think it's awesome when people customize and extend the plugin, and share that code with others. Since you posted the code here, anyone who wants to can copy it and set it up on their site too.
I think you could extend the bgmp object from another file just by doing something like,
bgmp.addFullScreen = function()
You'd just need to make sure that you wait until after bgmp.init() fires.
You might need a new hook inside buildMap() in order to call the function at the right time, but you might be able to do it from a separate file after the map loads.
In version 1.9 there'll be a bgmp.map property, so that you can access it directly.
If you attempt that and end up needing any hooks inside the core functions.js file, let me know and I'll add them to the next release.