I've been able to download steam mods before with SteamCMD, but Factorio's mods aren't on steam, they're on the official website.
To download mods from the official website, you either have to log in with a steam account that owns the game, or create an account and link a steam account that way. (You can also download them in-game, but that requires a steam account owning the game as well.)
Does anyone know of a way to download any of them?
This. The devs have no issue with piracy and would rather you pirate their game than buy it off the grey market for cheap, and their game comes DRM free anyway.