I've done the Jet Blue JFK trip a lot, so here's my opinion...
The Air Train to Howard Beach, hop on the LIRR to Penn Station (34th and 7th) takes about 40 minutes total. IMHO, it's the best option to get out to JFK to catch your flight (though probably *not* at 6 a.m.!)
Cab to midtown can take anywhere from 35 minutes to wanting-to-stab-your-eyes-out-hours. It's impossible to say, but it's usually not that bad.
The Dial 7 and car services like that are ok, but they tend to advertise a cheap fare, then charge you "waiting time" and things like that. The cars aren't that nice and you're not really saving money, so I'd go with a yellow cab over an advertised car service if those are your options.
The lines at JFK for a yellow cab (especially at the Jet Blue terminal) are not crazy, and it's well organized, with porters there to facilitate. Traffic going into the city at 1 p.m. won't be bad, and going back out to jfk at 6 a.m. won't be bad either. The only thing you would never want to do is try to take a cab to JFK on a Friday afternoon in the summer and sit in all the Hamptons traffic!
If all the bags will fit in the trunk of a cab, I'd just go for it (especially with 2 people sharing.) Bridge toll + tip = $55-60 total. The Air Train is $5, the LIRR is like $5 or 6....
Long winded reply! Hope that helps.
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