If you logged and saved all the files the first one requested you could potentially make it work. You could manually change of the file paths in the html if you only doing a few of them. There's only like 10 or so paths that would need to be modified. The PHP ones are likely harder to make work as php is a server side language and you don't likely have easy access to PHP server and everything that goes with it.
Anyway thanks for the link to to mynoise.net. It looks like a well designed, carefully crafted website.
It's an open source solution designed to scale to what the web was originally designed for and excels at. Documents. Specifically hyperlinked documents or webpages. You can't reasonably expect an archival service to archive something that is by definition not static like an interactive web app.