I would really pay attention to what your girls are saying and then see if there are substantive things that can be done to address their worries. Connecting with the best friend's family and coming up with a mutually agreed upon game plan is certainly part of the solution.
I was a pretty popular girl in K and first grade with lots of friends in a small school in a small town. When I skipped, there were definitely social consequences. My old friends didn't want to associate with me anymore and my new classmates were very cautious with me, never letting me into their inner circles. It was hard to find real friends after the skip. I became much more introverted, less socially confident. I did recover, but not until high school. I probably learned some good social skills in the process. It wasn't the end of the world. But it was still a big deal to the little girl I was.
My totally informal observation suggests that I am not alone in finding that girls in small close-knit schools who already have established social networks may suffer significant social consequences to their skips. So I would take the concerns seriously, don't just try to sell the skip to them. Listen to what they are telling you.
