Yeah, my 3960x allows PCIE 3. It's been a good minute, but I had to tweak some stuff to allow it.
I think it came down to something about the 3930k/3960x having the capability of PCIE 3, but that it was never full proof tested (quality assurance) and thus never turned on by default? It's been years since I did whatever tweak I found to turn it on. Not sure if the 3970x had to have a similar thing done or not.
Edit: Oh, and I wouldn't replace a 3970x at 5GHz in today's world unless you're wanting more than 6 actual cores. That's a very impressive OC, btw. I had my 3960x at 4.6 for a few years before I got tired of the heat it dumped into my room haha.