First off, the XMR_stak_cpu application is a CPU miner, so i don't think that doing anything with the GPU Drivers will affect it.

If it is the 3rd party miners that are crashing, and they only crash when elevated privileges are enabled, then maybe you could try two instances of the NiceHash application, like the following:

1) In NiceHash settings, enabled "allow multiple instances"
2) Launch two instances of NiceHash; launch 1 instance with elevated privileges and launch the other instance without  elevated privileges
3) In the NiceHash instance with elevated privileges untick the GPU so that instance only controls the CPU mining
4) In the NiceHash instance with regular privileges untick the CPU so that instance only controls the GPU mining

In this way, you will have an elevated instance controlling the XMR_Stak_CPU miner, and a regular non-elevated instance controlling the GPU miners including the 3rd party ones.