Looking at the all in costs of starting in different countries on my xONEx, I considered Jordan, which would force my Iraqi flights off the ticket because of the no-transiting the origin rule. Though I knew it wouldn't work I tried to price out an ex-Iraq trip, which validated, but failed after pressing "Book Now" with the error:
Sorry, there was an error. The booking engine could not be contacted: Object reference not set to an instance of an object.
I don't know if there are any places you can fly to (that appear as destinations on the tool) but not start from on an xONEx, but this would probably hold true for those as well?
Also, regarding the illegal QF codeshares of AS flights showing up, this might be fixed (sort of) in that they appeared for me but if chosen bring up:
Due to traffic restrictions on this flight you must be booked on the operating carrier. Change this segment accordingly.