I think the zine version's printing instructions may be wrong? I used a lot of paper wondering what I was doing wrong, but it turned out that as soon as I switched to "Flip on Long Edge" instead of "Flip on Short Edge" as instructed, everything worked out perfectly.
Also, for people who use Letter rather than A4, the combination of printer margins and the difference in paper sizes will cause the folds to cut pages in the middle of pictures/text. The best way to avoid that is to not only shrink to fit, but also turn on bleed marks, and then trim the pages according to the bleed marks.
When you do that, the result is wonderful and super cute! My partner was having a bad day, so I gave it to her as a present and she was very happy. :)