I did some research and found out that I can indeed apply textures to lights (special materials called "light functions") and this process if perfect for achieving a cucoloris effect. You can see the results in the screenshot below. I've left the effect pretty subtle, but I think it gets the job done. Let me know what you think.
You'll see below that I'm also experimenting with some in-game post-process image grain. Opinions on that are welcome. It gives a sort of "TV" feel to it.
(You can get a better sense of the image grain by clicking on the image below and viewing the image at it's original 1920x1080 size)