How do I copy files I downloaded from the wayback machine to my new site?

I don’t know that you can do that. WP files are stored in the database. The Wayback machine is just a generated version of the files.

You need the database. Your hosting place might have a database backup, though. If you can get a backup copy of the database, you can use that in a new Drupal install, then export/import into WP.

Maybe.

Otherwise you could ‘scrape’ the Wayback site for the pages, but that will just give you a static site.