I have decided to sew the prairie points to a one inch strip of binding. I will have them the proper distance apart so they cover the edges perfectly, and I won't be taking the quilt apart.
I will then press the seam allowance over and attach the other side of the strip to the edges of the quilt top. Then I will sew a matching, pressed binding strip to the backing. I can sew it shut all the way around (through the binding strips) with the points sticking out.
I think this should work.
Thanks for all the suggestions!