Using CUDA rendering on 970 and 560 Ti after driver 361.45.18 error: invalid device

It’s been a long while since this behavior started, so I don’t know if someone has reported it before me.

Hardware:
AMD FX-6350
16 GB Kingston ECC ram
970 4 GB in the primary slot
560 Ti 2GB in secondary slot
Dual screens on the 970

Centos 7.3
NVIDIA binary driver 384.59
Latest working driver 361.45.18
CUDA Toolkit 8.0 (7.5 also presented the problem)

After driver version 361.45.18 (including current 384.59), CUDA rendering through Octane or Cycles will cause one or both of my cards to fail, requiring me to restart the application with a different card configuration before I can use them again. In short, I am able to use either card individually, but I can never use both cards together. This is obviously not a SLI problem, but both renderers used to let me use both cards. As far as specific errors, I attached output from both renderers; the first section is all Cycles, while at the bottom is Octane’s log output.

I’m not sure how else to describe the problem. Even the simplest scenes cause a problem. I’ve tried the same thing on Windows in a 372 driver and it works as I would expect. I posted about it on the Octane forums and it seemed other people had a similar problem, although we never found a solution other than a clean OS install (which I can’t do).

Relevant threads and pages:
https://render.otoy.com/forum/viewtopic.php?f=13&t=58615 (may need an account + product to view)
https://blender.stackexchange.com/questions/68186/gpu-rendering-fails-with-cuda-error-at-cuctxcreate-invalid-device-for-gtx-960
https://developer.blender.org/T50232
nvidia-bug-report.log.gz (279 KB)
software_output.txt (51.2 KB)