I used to suffer from migraine. It stopped when I reached 50 although I still get headaches.

I wouldn't have tinted glasses or add on filters. An LCD might well help - you say you find the one at work better so that is rather conclusive. I use the 30" Apple Cimena screen but the Dell 30" is supposed to be just as good and significantly cheaper. Remember you would also need a dual VDI to drive a screen over 1920x1200.