Thanks for playing!
I do actually test on a real GBC, along with an analogue pocket (and yes, a GBA), using an everdrive.
Unfortunately there is no “real”, fixed palette I can go for - especially in the current era where everyone is using aftermarket screens.
I recently taught myself GLSL and started implementing shaders in the online emulators, as well as trying other, non-shader approaches.
I have an (in-progress) emulator at http://www.jmkdev.net/assets/gbtest/ that attempts to simulate a GBC screen more faithfully; you may have to enable controls and set the system to GBC instead of DMG. I’d love your take on how well that matches your GBC experience.
I also have another emulator in progress that has a slightly more complete version of the effect: https://i.imgur.com/4o7ppYv.png
But that one isn’t publicly available yet.