If you miss your connection, all you need to find is an F seat on any reasonable to connection to any New York area airport. There are PHX-JFK flights you could take, as well as connections through DFW, LAX, PHL, CLT, ORD, or MIA among many others.

In addition, the first flight in the morning is going to be generally your best bet to avoid delays. If it is delayed, it's often because the crew arrived late the previous night, which gives you time to rebook before you leave BUR (you could take a flight from LAX, for example).