Whoa! $65 to go from LGA to JFK - somebody sure did get ripped off.
I usually use those $11 Port Authority Buses if I have time and they run every half hour and take about 45 minutes to go airport to airport with a stop at Jamaica Station on the way.
Yellow Cab - you just have to act like you know what you're doing with these guys. If in a hurry, I jump in, say "JFK, Grand Central, Van Wyck, I am familiar and you check with me before taking any short cuts!" They get the message. Average cost about $25 (22-28 depending on traffic). Just make sure you have something close to exact change including tip. I love when you give these guys two twenties and suddenly they have "no change". I had one guy pull that stunt on the $22 ride over. I pulled one of the twenties back, grabbed two ones out of my wallet and said "Sorry, if you had change you would have gotten a two dollar tip - them's the breaks". (He had change and realized he just shot himself in the foot.) They usually don't mess around too much when you are in uniform and act like a New Yorker.
Any year now, they'll get that great boondoggle in the sky known as the "Airlink" finished - Great link from Jamaica Station to JFK. It was supposed to be built from LGA to JFK but they ran out of funds! (Say with heavy NY accent) ---> "Go fig-yurh!"