I am currently a Delta ER pilot at JFK and have a crashpad in Kew Gardens.
The MTA bus (Q10) goes from term. 4 JFK to Kew Gardens. If you buy a Metrocard it's $10 for 12 trips. They have an express service called the limited that will get you to JFK in 20-25 min, regular service 35-45 min. I have used the bus as early as 0500 and as late as 2330 and have never waited more than 10 min.

On short call the "readily available" clause can mean different times for different places and weather. There are guys sitting call in the Philly area and have no problems. Add snow etc. and everything changes.

ps. Terminal 4 at JFK is next to Delta's terminal (if can call it that).