Have you tried holding a small section taut between your hands, front and back, and sewing small spurts at a time?

You could try starching it. I would assume you plan on washing them anyway. I've also cut strips of sticky washaway stabilizer to place along the edges of minky fabric because it stretches so much. This is what I've used: Sticky fabri-solvy. It's available at Joann's.

If the two layers are slipping, try water soluble fabric basting glue. You could also hand baste; it sounds worse than it is. If the fabric is slipping in the machine, tissue paper can work.