Hi Ben,
I often take the whole MAXON folder and move it. Anything that C4D needs natively is in this folder normally. You need to have your serial numbers of course.
The download for customers is a different one than the one I have to use, so I can’t really tell how to re-download again.
I would say, give your Rep at MAXON an e-mail about this, or check with the support directly. There is certainly a way, if the one above isn’t working.
http://www.maxon.net/en/support/support-questions.html
Congratulations to the machine!
All the best
Sassi