Nice post, Will!
Oh, Forrest, if both of your routers have the option, try configuring your first router to have a DMZ host (being the second router), and the second router having one too (being your computer).
I know that it might not be required by some FTP servers, but have you tried including the port number in your FTP call, such as ftp://[server]:21/ ?
Also, there might be some kind of configuration you need to properly set in one or both of the modems (could be firewall, restrictions, or general networking options).
If all else fails, you might want to try reading up on the router manuals/help resources and learn as much about any software you're using to make the FTP server.