Update: I ended up not using batting, although in retrospect it probably would have given a nicer drape. Warmth was not a concern for the intended recipient.
Because I was doing a quick turn, there was no opportunity to spray baste the layers, which would have stabilized the fleece. It came out okay nonetheless, and the recipient loved it. She is hoping it brings luck to Alabama this weekend!
My favorite part of the quilt was the FMQ A's at the sashing intersections.
Thank you all for your suggestions!
Next time I use fleece backing I will layer it in the traditional way, with batting and spray basting and binding.