With that many layers you really should be using a sharp needle. A universal needle isn't quite sharp, isn't quite ball point so it's universally good for nothing. Go back through and oil the machine well again paying attention to the making sure the stitch length lever moves freely but not loosely and stays still when you put it in reverse. Run it in for a few minutes to let the oil get in where it's supposed to go. Try some test stitching. Does the bad reverse stitching happen at the beginning of sewing or at the end of the seam? I'd be more inclined to think it's a feed dog issue.
Cari