my school, which generally knows what it's talking about with oxbridge admissions, told us that from past experience that if two people applied for the same course at the same college, the lesser of the two would be rejected/pooled even if they were better than the applicants from other schools. They take this quite seriously- to the extent that that they put up lists of everyone applying (generally about 150 a year) and the subject/college they're interested in, and make sure any clashes get resolved.
I'm aware this goes against the admissions policies, but i'd be very cautious of applying to the same college as the other girl- even if they would be willing to take two people from the same school, do you not think it'd make things really awkward if one of you got in and the other didn't?
If she's unwilling to change college, and you still want to apply to Johns, could you get your head of sixth form to flip a coin over it? At the end of the day, college choice isn't as important as it's made out to be, and many people just choose them arbitrarily anyway.