I'm certainly no expert on routing, but is there a way on Westbound to go from EUR to SJU without a USA/Canada touchdown? Say: EUR-SJU-LIH-LAX and onward? This shouldn't violate the rule.. Or perhaps, if added to a SA itinerary, like EUR-SA-SJU-LIH-LAX.... Hmmmm... Not that I plan to do it this trip, but love a good puzzle!
Robin