I think I would first check my cutting for accuracy using a non-acrylic ruler. Then I would check my pressing to make sure it's clean and crisp (maybe try open seams). After that I would possibly change my thread thickness.
A zipper foot only gives stability on one side, not the best way to maintain a precision edge even if you're sewing with the foot to the right (on the seam allowance). I use an open toe embroidery foot and shift the needle to get what I need with visibility, stability, and accuracy. Good luck to you.