Anybody try a taxi and Air Train option??
The fastest way to get from LGA to JFK is by taxi, unless the before mentioned shuttle bus is ready to leave. I have waited for the shuttle bus for over one hour before the correct LGA-JFK bus arrived.
One possibility is to take a taxi to the Jamacia Train station and then catch the JFK Air Train to the correct terminal. This could theoretically save time if the Van Wick and/or terminal loop is backed up.
I agree with the abover posters, this cnx is a little on the tight side. Could be impossible if the OP has no status with the JFK outbound airline.