So don't do a 45 degree perfect crosshatch.
You can do a straight horizontal/vertical, and that would match up.
You can use the same color thread as the fabric, and that won't show up so blatantly.
You can fold the piece, make registration marks (taking into consideration the seam allowance, whatever size it is),
and then draw your grid for the cross hatching.
Or just do free lines from side to side from (still using the walking foot if you don't want to FMQ) as long as one line begins on a registration mark on side A, and ends on side B (this would be my personal preference).
Pic to follow