I do a lot of spirals. Spirals, especially small ones, have tended to exhibit the sort of cut-through problem you described. The slightly-offset double-cut approach has worked well for me on some of the more challenging ones.
I know it’s a lot of work when you are doing 168 cards but, you can often rescue some of those that have a few issue with a sharp craft knife. If you are gentle, the partial cut will guide you along and, it won’t be noticeable. I use a translucent self-healing cutting mat on top of a light panel so I can see the problem spots easily.