I swapped back to my original video card, old drivers and original screen and cables and was still experiencing some of the headaches, although not quite as bad.
I've just been to get my eyes checked - and well, it looks like I need glasses from here on out.
That means I'll have to reserve judgement on the issues I've reported (many/most LED screens, PWM, CCFL vs LED backlights, stresses over certain video cards etc) until I get those dialled in. I do still expect that LED screens are going to be problematic but I'll be intrigued to see what if any issues follow once I'm used to the glasses.
I'll be sure to report back here.