I'm in a somewhat similar boat - I'm trying to understand the rules behind booking EK. JFK-ICN seems to be allowed as JFK-MXP-(PAR/ATH/xxx)-DXB-ICN, but I can't fathom how you could possibly transit between MXP and PAR.
Also, AS's website doesn't seem to allow me to search DXB-ICN, I always get an error. Can I only search itineraries that originate from the USA?