Green Card holder as well (soon citizen). I used to be able to OLCI on my returns to US, now I can't anymore (for at least a year).
It recognizes me as non citizen and asks for date of return to country of origin. Of course I don't have one. I even tried to put my green card expiration date and that would not do it. My friend who was returning with me from Singapore last week (also green card) could not OLCI either.

I'm curious to learn from cfisher's experience. I have never found a field to enter my green card online. Only my passport and GE info.