Ryan, I ended up just moving the site over to our Rackspace server. It works perfectly well there.
Without getting too technical, I think it was a combination of the PHP version, Magic Quotes, and an issue where the php.ini / htaccess methods of turning off Magic Quotes was somehow not allowed by the server.
I don't think that you have to worry about this as being a bug that needs to be fixed, I think it was an unreasonable server configuration issue.