I'd sewn perfect zips for 30+ years until I bought a machine with a clip on zip foot, it was impossible to sew past the zip pull as the back of the foot is too wide. So I used my screw on adjustable foot instead of the one that came with my machine

This foot is for low shank machines. See image.
It allows you stitch up close to zip teeth without having to open up the zip.
Doubles as a piping foot as well so there's no annoying gap between your pipng and the seam, nor do you need different sized piping feet.

Narrow Toe Adjustable Zipper Foot