When using Windows, screenshots are captured with your monitor profile embedded, rather than the correct image profile. And you're right, this is definitely a problem.
However, I've never explored third-party screenshot apps. Maybe there's one that captures colours correctly?
Two layers:
First, a Channel Mixer layer at 60% opacity:
Green channel changed from 0/+100/0/0 to 0/0/+100/0
Then a Hue/Saturation layer at 100% opacity:
Reds 0/+25/0
Cyans -10/-60/0
Learn more about this in the Creativity Class.