Thank you for your answer (and explanations), Alen.
Sadly, it’s still not showing any more results on the archive page.
I usually do the re-saving the permalinks “trick”, although I haven’t saved as default and then re-save as post-name. In any case, that hasn’t helped either :(
Here’s a gist of my custom functions file and my archive file (in case there’s any weird conflict somewhere I’m not seeing): https://gist.github.com/swthate/0fbd3a449455c9ddbf1a
If it’s any help, I’m using the FoundationPress theme as my starter theme.
If my posts per page function looks a little different from the one you just posted, it’s because yours unfortunately wouldn’t work, so I tried the code from the StackOverflow answer again (even though they’re the same. ugh!)