From what I read, DYKWIA chuck1 meant something else.

I think chuck1 arrives to JFK on another airline, and he's asking whether the chauffeur drive (EK's) can be used for his arrival on the other airline instead for his departure on EK202 back to LGA.

I don't think EK allows for this. As for booking the chauffeur, anyhow it can be used up to 5 hours before departure time only (7PM in your case).
Besides when you book the chauffeur drive for your departure, they will ask for the pick up point, and it can't be JFK itself (unless it's a different terminal as far as I estimate).