Sorry, I wasn't completely clear.
My directions for spray starching were for not taking the entire quilt sandwich apart. If the puckering isn't too extensive, I would probably take out the stitching in one area and try the spray starch approach in that area to see if I could then re-stitch it without puckering. It seems to me it might be possible to take some of the excess fabric out with steaming, and then the starch would help keep the backing from re-puckering when you repair that area.
Incidentally, I didn't realize there was a second page to this thread until after I posted. I prefer cotton battings, so didn't realize spray basting doesn't work as well with poly battings. The spray I use is from JoAnn Fabrics and made especially for quilt basting. This has never gummed up my sewing machine needle.
Mary