I've been working with my host for the past week to try and diagnose what could be causing 404 errors to not show up. This is what he said:
Looking closer at your message, there is no 404 happening, because the index.php file does exist. This cannot be fixed via IIS, it must be done inside their application. See this for example:
I can paste this link if necessary, just didn't want to spam.
Given my limited experience with PHP, I don't know if this is even possible to fix, let alone how to fix it. Does anyone in the community here have any insight on this?