The solution to machine foot marks is to hand stitch it. I worked in a saddle shop when I was younger and all assembly was done by hand. We did use stitching machines to punch holes on things that a few marks wouldn't hurt. Hand stitching is stronger so we did that so it would last as long as possible.
The advice already given on the order of things is good. I always stamp the designs first. Then, depending on the project, I may dye before or after assembly.