Excellent decision about the mountains!
How about the two purple and a white strip border with each strip in the same width as the star points, but mitering the corners instead of the nine-patch cornerstones. The miters would mirror the onpoint star blocks and the strip width would repeat their size. It would be both a visual continuation and a frame at the same time and should make it the size you want.
My worry about the nine-patch corners is that there is nothing at all square within the large center of your quilt and they would look quite out of place making their first appearance way off in the outer corners.
Adding just another row of stars and no borders is a good option as well. That center can easily stand on its own with just a purple binding.