Looks like *A has NYC - DXB for ~$2.6k right now with a decent variety of *A airlines to choose from (TK, LX, UA, AC). Not quite as low as you are looking for but decent.
Wait and see if BA matches and then buy an AARP membership for $16. That'll save you $400 on a roundtrip flight which would take it down to $2.2k (again if and only if BA matches)