I took a few minutes to check mine out (again- I had a code thrown from a taillight for high resistance not so long ago) for you Kat, with a few photos. To get to this point right here, no exaggeration, I think only about 5 seconds. The panel pulls right off (pull outer edge towards the panel's center, putting a thumb right at where each "tooth" would probably give you easiest success; either side works, but it might be easier going "away from you"?).
There is only one little gray tab to depress and the socket panel comes right out. To unplug the plug, I remember that being a bit difficult, I probably had to use something to help depress the tab to do so, but it's not necessary here anyway for you. Tip, when you're all done and putting it back together, make sure to double check that the socket is snugly in place by pulling on it. It's weird how it always takes me a few tries, even if every try really seems like "oh, it's gotta be in, right?". I'm thinking it might help to pull the tab vertically to help it "snag" or something, not so sure.
A better angle at a couple/few apertures you have to work with:
This is using the "flex neck extension wand"
that came with my Metro Vac, to see if it would get in there.
I think it can get to most* places inside (I did play around with a bit) and the one thing on my side (if I was in the same predicament) is that the suction power would be pretty strong with the machine, given the small aperture of the wand.
Anyway, andrew's idea is definitely worth a shot, you could be done within minutes, if you're lucky that is. Good luck, and nice flake in your paint! What LSPs am I seeing there?