(This was originally why I posted. But I figured it out, and am putting question and solution here.)
The first portion of my problem was that my display contrast and color depth was way off. I had been using these Test Images (Contrast, Black Level, and White Saturation pages), and it looked as if all the colors were squished into RGB 20-235 and everything outside of that range is assumed to be the extreme value (0 or 255).
The problem turned out to be that my monitor was set to Limited RGB 16-235 the whole time. Switching it to Full RGB fixed the color contrast.
In conclustion: make sure that both your monitor and graphics settings are set to full RGB.
The second portion of my question is about how to set ICC color correction on Linux. I already have an ICC profile for my monitor.
What is a good way to install it?
I am running Arch Linux x64 with an Nvidia GTX970 graphics card connecting to my monitor via HDMI.
I have nvidia 375.10-1 proprietary graphics driver installed, along with nvidia-libgl and the nvidia-settings tool.