The 77W could definitely do it. Although even on a good day the RTOW would be restricted to 10 tonnes below the MTOW ex NBO.
Assuming there isn't alot of cargo in the hold destined for JFK, and mainly just pax and their baggage then the aircraft should be able to take off from Jomo for a direct flight to the U.S.
I have no idea about the numbers on the 788 but i strongly suspect the 77W has better performance and range.