Birthing quilts always gave me the same problem. If you intend to use ties then yes they need to be 4 inches appart as recommended by the batt.
If you decide to machine quilt, you can try this. Smooth out the sandwich as best you can easing the extra fabric to along all 4 edges. Pin the sandwich well and quilt the middle leaving 4 inches all around the edge. Place quilting motifs at intervals around that last 4 inches. It will be quilted but the spaces will allow the extra to puff between the motifs.
You can also quilt the center up to the last 4 inches around the edge, rip open the side seams, smooth out the quilt edges, trim and put on a regular binding.