"my only thought is to quilt the center and then take off the frame and float the top to do the edges?"
This is also the only way I can think of. I would cut the batting narrower so that when you fold the edges up there won't be as much bulk you have to deal with. QUilt to within a couple inches of the batting so you have room to attach the new pieces before you turn & float.
I also have a 10' frame and my sister wants a large quilt for her king. What we had talked about was leaving the side borders off, quilt the center, then quilt the border sections separately and join using a QAYG technique.
Good luck! Let us know how it goes.