Found the instructions on how to install without ssh access:
http://archlinuxarm.org/support/reinstallation
A few things to remember if you're a noob like me:
- You have to be root when doing this. If you're in ubuntu sudo will not work. Sudo su will.
- Make sure the file download link in step 4A is the actual link for your particular platform, and don't just copy / paste the link shown in that step.
Follow each step correctly and you'll be back in business.