Can't Download Mavericks via App Store nor Upgrade from OS X 10.8.5 -- Command Line Installs Not Supported
This isn't the ideal path, but you could always boot to the Recovery HD and re-install the OS to an external USB drive. Your Mac might re-download Mavericks directly but more likely would re-download the version that created the Recovery HD.

At that point, you would leave your internal drive untouched and install a clean system on the external drive.

From there, you would be able to boot off that external drive that doesn't have the new iTunes and download Mavericks. Once you had the installer, you could run it against either the internal drive or the external drive and migrate data over if you chose to upgrade the external to Mavericks first.