Thanks for the BIOS suggestion. The latest update (2013.09.18) actually mentions the E5-2680v2 in it's release notes:
Addressed an issue where a system configured with Intel Xeon E5-2690 v2, E5-2680 v2, E5-2670 v2, and E5-2660 v2 processors and Advanced Memory Protection configured to Online Spare Mode may experience incorrect behavior when multiple Online Spare switchovers occur on the same processor.
So the processor itself seems to be supported.
For the heat sink: I guess I'll order try it with the Intel one, and if that doesn't fit, I'll order the cheapest available HP CPU kit and use that heat sink on the new processor. I'd be more than happy to hear from anyone who's convinced that this isn't going to work, though. (I'm not asking for guarantees, I just want to make sure that I'm not making obvious mistakes.)
Thanks!
Koen