I had not purchased by Allianz policy yet. It was an option that was available to me from Priceline when I made the booking. That's why i'm looking at rentalcover.com as your suggested. I see that the CDW is definitely cheaper but there seems to be some discussion as to whether it is actually better than getting it directly from the car company.
You've also hit upon another worry of mine regarding using university contract codes. I found a code on my university website

and was actually able to make a booking and nobody asked me for a proof. I have very few days to go so not sure I can find a way to get an approved document that actually states that I'm an alumni. I do have a scanned copy of my granted degree (in fancy latin and everything). Wondering if that will be enough. It's a long rental so I really don't want anything to go wrong on the day of picking up. Worth it to call the rental car company to confirm?