My contract arrived this morning, during my mom's birthday lunch. As soon as we got home, I downloaded and filled in every remaining form that I need to fill out, including the SARS stuff for the tax exempt status.
Now it just needs to be sent off. Hooray!
My recruiter provides a very helpful guide for filling in the visa form, although the section numbers don't quite correspond because they just released a new visa form. A skype call later, though, every tangle was sorted.