I would like to add that the problem appears to be resolved on my installation
of Ubuntu 18.04 with the MSI R9 390 8GB GAMING GPU using the current mainline
kernel (4.17-rc4,) with the kernel flags of "amdgpu.dc=1" and "amdgpu.dpm=1".
Clock scaling appears to be working as expected and I haven't had any visual
artifacts or crashes to speak of yet. Using "amdgpu.dc=1" alone didn't make a
difference but, "amdgpu.dpm=1" made all the difference.

Good work to everyone involved!