Your GGD must be loving that quilt every day, all day - and that's a good thing/big compliment to you!
Minky will make a wonderful new backing. And the quilt will be warmer as well.
Flannel is one of my favorite backings, but I have never done quilt as you go, so can't comment about that technique. When I use flannel for backing, I generally will seam two pieces together and then LA quilt.
I read early on in my quilting career that flannel must be washed and dried twice before using, so that is what I do.