I tested the nouveau module built from https://github.com/skeggsb/nouveau on
top of the latest drm-next kernel and I can confirm that it fixes the black
screen issue on my GTX 970 with 4GB of VRAM.

Ben, would it be possible to extract the relevant patches and backport them
onto recent stable kernels such as 4.9 and 4.10?

Haven't tested Lyude's patch yet.