Do you have a solid darning/ FMQ foot? My Bernina has a round dish shaped foot that keeps the surrounding area by the needle down and I would use that. If you don't have another foot, I might try laying a sheet of tissue paper over the surface, quilt through it and remove it after the quilting. As for quilting it upside down, I would put the tissue paper under it so it didn't catch on the feed dogs if you can't lower them.