Newark to JFK

Hello all,
Does anyone have any experience of inter-airport transfers in New York.
I am arriving into EWR at 9.40pm and have a morning flight on the VS26 back to LHR from JFK (departing 7.40am).
I am thinking the best way is probably to get straight over to a JFK airport hotel and get some shuteye. Will a normal taxi happily do this trip (any idea on cost?) - presumably I could get dropped straight at the hotel.
Alternatively are there any reasonable transfer companies that offer such (private) transfers - I don't really fancy hanging about waiting for a hotel shuttle at the other end.
Alternatively I suppose we could stay in Manhatten and get an early taxi - the VS26 is on a Sunday morning so presumably traffic won't be so bad at 5am.
Does anyone have any experience of inter-airport transfers in New York.
I am arriving into EWR at 9.40pm and have a morning flight on the VS26 back to LHR from JFK (departing 7.40am).
I am thinking the best way is probably to get straight over to a JFK airport hotel and get some shuteye. Will a normal taxi happily do this trip (any idea on cost?) - presumably I could get dropped straight at the hotel.
Alternatively are there any reasonable transfer companies that offer such (private) transfers - I don't really fancy hanging about waiting for a hotel shuttle at the other end.
Alternatively I suppose we could stay in Manhatten and get an early taxi - the VS26 is on a Sunday morning so presumably traffic won't be so bad at 5am.