After a very period without the ability to post via Blogger.com, the problem is finally fixed. It turns out that the problem was really an issue with the perimeter firewall blocking certain ports, which, under normal circumstances, wouldn't need to be open. In fact, normal FTP clients need just one port, while Blogger needs over 64,000!

After analyzing network traffic directly on my server a dozen times, I finally looked on the perimiter firewall... to no avail. I turned the firewall off, and voila! Blogger worked! In the help for Blogger, it says:

Additionally, ports 1024 and up must be enabled for these IPs, for the ftp connections to work properly.

Seriously, it should say "ALL PORTS ABOVE 1023 MUST BE OPEN" Because it's really that important. Of course, if Blogger was using a real FTP client, and not it's own special one, this wouldn't be an issue.