After re-running quickpkg, I still get no "binary"s in the emerge output dependency tree.

At some point, I started getting 304 errors here again.

304 Not Modified

This is used for caching purposes. It tells the client that the response has not been modified, so the client can continue to use the same cached version of the response.

I suspect the problem is related to this.  The Packages file is the package index file.

# ls -l /var/cache/binpkgs/Packages
-rw-r--r-- 1 root root 1024590 Apr  4 13:00 /var/cache/binpkgs/Packages