It appears that the phone boot-loops for a bit until it lands in into ClockworkMod Recovery v188.8.131.52. The CyanogenMod logo appears at initial boot.
This recovery tool seems to have no external microSD card access. I already have ADB on my Win7 machine and was able to install a driver for the S3 to allow me to sideload via command prompt.
I attempted to do this with a copy of the stock ROM without root access.
Initially I was forced to update a line on the script to bypass the invalid number of arguments roadblock, but later encountered this:
Finding update package... Opening update package... Installing update... set_perm: some changes failed E:Error in /tmp/update.zip (Status 7) Installation aborted.
Thanks for the brainpower