I've done cross hatching on several quilts - in fact, it is one of my favorites stitches when using my Singer 201 to straight line quilt. Like you, I use painters' tape and my walking foot. I lay the tape diagonally from corner to corner on the quilt. To make doubly sure it doesn't move, I also pin it every few inches. After sewing the first two lines, I have a big X on my quilt. For subsequent stitching lines, I just keep moving the tape over from the stitching lines made by the big X.
I always glue baste my quilt layers before quilting. I've tried other methods, but like the glue basting best because I never get any puckers in the front or back of my quilts. I put Elmer's School Glue in a carpenter's glue roller bottle and just roll it onto the batting, then smooth the quilt front onto the batting. I let that dry a few hours, then do the same with the quilt back. Carpenter's glue roller bottles are available on Amazon:
https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1