Originally Posted by
Middle_Seat
... but (if I accept the suggested times for NY Airport Service shuttle) I would have only 45 minutes between drop-off and pickup in Midtown!
There's your first mistake.
As I mentioned in my prior response to your inquiry, you can easily have three hours in Manhattan if you're interested. But it means taking public transportation (a very easy hour long journey) back to JFK, and not a van service that's at risk of sitting in very heavy rush hour traffic.