I have The Cold War Deluxe, Rise and Rule v.1.02 (C3C), and Rhye's of Civilization - the fastest loading mod. I'll check my old install to see if I had any of the others at that time. Some of them have been re-uploaded to external sites with links near the end of their threads; this is less than ideal as they both become hard to find if there are more replies, and sometimes those links stop working too. Fixing the Downloads Database with locally hosted versions is an ideal solution.
One small note, The Cold War Deluxe is actually by El Justo, and its Downloads Database entry links to El Justo's thread. I believe what happened is that back in the vBulletin days, there were separate "Uploader" and "Author" fields, and in the migration to XenForo, the "Uploader" field survived. Most likely, Red Door added the Downloads Database for the mod once the Downloads Database came online. I don't know if there's a way to change that, and it's not really a big deal since the thread makes it clear enough, but perhaps that could be updated at the same time.
is still active here, and might have his Haile Selassie leaderhead. I feel like I've seen that one around too, though I can't quite place where.
On the topic of broken Civ III links, I was looking at the Civ3 Screenshot of the Day page
recently, and realized almost if not all of the screenshots still exist on the Internet Archive, but aren't on CFC anymore. I archived the first 30 days' worth locally, and if there's interest I could collect the remainder and potentially fix all the links.