Add in some more light sources around the display that stimulates sunlight (something like CoeLux) and you might be able to get at least the mood benefits and some of the health ones too.
Artificial sunlight therapy is frequently used in countries that gets very dark during the winter, where there isn't many sunlight hours. I remember some friends many years ago went to those kind of therapies in the winter times and felt benefits from it. Not sure exactly what light sources they used, but if you can manage to buy those, maybe it'll be at least a bit better?