Thanks for all your help and suggestions.
So far, I have used fusible web under all the sticky-uppy edges and that has already made a huge difference. The two places where whole blocks have almost come away, I will habd stitch down and the 3 blocks that are beyond either of those I will use the tulle.
Or do you use the tulle over the entire thing? And can you machine quilt over it?
Here's a block I've repaired so far. I'll still do a serpentine quilt over the seams.
[ATTACH=CONFIG]554826[/ATTACH]
[ATTACH=CONFIG]554828[/ATTACH]