If in the fic the Fellowship goes through Moria, I have an idea. You could use your Khajiit (I forget his name at this point). Khajiit have always been masters of stealth. So you could have him hide in a dark corner wait until the Fellowship passes, snatch the Sue then retreat into on of the darker recesses of Moria. Alternatively any sufficiently dark area could also work.

Does she go off to angst or something at any point? Could you carry the mission that far?

Failing that, I think the single combat idea could work. The Fellowship would likely respect a request to keep out of it, especially if the Sue herself makes it while they're still under her control. Of course, the agents could have a bit of peril once they kill the Sue if the characters don't snap back into character immediately. That could be fun. OTOH, there's no real reason killing the Sue shouldn't allow the canons to return to their proper characterizations in a Mary Sue mission, so you could avoid it if that's better for the story.

~Neshomeh

An important question is, does she at any point in the badfic, demonstrate any fighting skills? Because some Sues will boast about their proficiency with a blade/bow/whatever but never actually show said skills. Which means you can take it all as being a lie; they have no idea how to handle a weapon and will be an easy kill.

As for how you get her away from the others, my agents usually just open a portal underneath the Sue and let her fall through into wherever they want her. It's not exactly dramatic, but it works and it's fast.