Well, the memtest ran for 7 hours, without any errors.
Nonetheless, I am getting more and more convinced that it is a hardware error, more than a software error.
Since the freeze happens mostly under a certain (known) load, I suspect the NICs.
I've changed the network configuration as a test, and will replace the NICs as soon as possible.

For the sake of shortening other users' problem cycles in the future, I'll keep this thread posted...