I don't know enough about the quilt as you go method to really offer an opinion. The only thing I can think to say against it as that it wasn't really a method they used back then...so it would sort of make it that much less "authentic" but I don't know that you, or any of us, is going for that. I also love to see the stitching on the back...
As for batting, I'll go with warm and natural, and likely am not going to wash. I did not wash my fabrics ahead of time. I also really, really want to just hang this on the wall, and it's likely I won't ever wash it. Some of my blocks are barely holding together, so it won't stand up to much abuse, for sure!