Sweet, looks like they got it fixed (for me at least). Highlights from the conversation:
Me - Using composer on my dreamhost account does not work where it recently did. Running it on my local computer works fine.
My guess is it's this problem that people are talking about, where communications using ipv6 are unreliable. Using v4 addressing works fine, so people are modifying their hosts file to force packagist.org to be requested using v4.
Me - "I see it showing the correct IP for both v4 and v6. The problem people were mentioning was that communications would switch between v4 and v6 for some reason and often fail when v6 came into play. So the hosts file entry was to force exclusively v4 usage."
DH - "I did confirm there's an IPv6 issue at our Virginia data center. We're currently working on resolving the issue."
DH - "Can you please give it one more try? There was only one broken customer ipv6 on the entire machine, which is now cleaned up and ipv6 is re-configured now. If something cannot connect via ipv6 now it should switch to ipv4 automatically."
I don't know what they ended up doing to fix it, but I hope this saves someone else the many many hours I spent fighting this issue.