I finally was able to book my EK F JFK-DXB-SIN for next april. It took about 12 HUCA til I found an agent able to find some availability as the website doesn't show anything past 3/28/15. What worked for me was the line "an agent was able to find space the other day. She tried 'something different'." After that the agent was able to magically find all sorts of availabilities for 2 ppl.

Thanks everyone on here for the help.