Does anybody know how to download the addons without logging into Bethesda.net? I've tried downloading one of the official addon wad files (in this case Anomaly Report) and putting it in my DOOM directory, but it's not showing up in the installed section.

Download them elesewhere.
Final Doom WADS aside, the rest should be available in well know sites, even the original Final DOOM DOS WADS should work in theory. The only difference could be the little files they added to the wads to show descriptions and the proper names of the maps.

Also downloading the mods from other sites will get you the unedited original versions of said mods.