Hi Soullessginger:
I might be wrong, but it looks like you are in the wrong section. You should not be adding Travel Documents in the section My Profile (where you input your travel docs for future bookings, to pre-fill automatically), but you should access the API Section in your booking.
You need first to pull up your booking in My Trip (either by looking up with your Last Name + Record Locator, or, if your FB number has been input, the booking should appear automatically in My Trip).
There, you go to Passenger Details, and there go to the API Section.
In my case, I have all three (passport, green card and KTN) there. See screenshots from my iPhone (I accessed klm.us mobile website via iOS Safari).