I've found a way around this limitation. The first thing you need to understand is that this is a limitation imposed because the install script needs more than 512mb of RAM to install correctly. Therefore, they require a $10 server as it has 1GB of ram.
An easy workaround is to setup and install an ubuntu $5 server (don't worry about which version, you'll be destroying it shortly). Then go into the droplet and do a FLEXIBLE resize to a $10 server (this will upgrade the CPU/RAM but not the HDD size). DO NOT CLICK ON PERMANENT RESIZE!
Once that is completed, go to the "destroy" menu under that droplet and rebuild it using the "Ubuntu Wordpress on 14.04" image. Since the droplet has 1GB of ram, it will allow the installation to progress.
Once that is completed, power off the droplet and do another flexible resize back to a $5 server.
Wordpress should run ok on a $5 server for most applications, so once the installation has been done on a $10 server you should be able to maintain your site on a cheaper server.