Yup, I'd take those extra hours in the air rather then a JFK-EWR connection with the amount of bags the OP has. No way I'd do the trains in their situation. I've done other JFK - North Jersey train trips when I used to live in JC and was fresh out of college (I.e, Airtrain - LIRR, then walked to PATH at Herald Square). Was painful, yes, but with little baggage, it wasn't too terrible.

Even without the amount of bags, other potential problematic issue is time. While 6 hours may seem like a lot, depending on arrival times and time to clear customs, get bags, buying each individual train fare, waiting for/transferring trains, then needing to re-check luggage - there's really not much leeway. Sometimes I did these trips at night and it was easily an hour and a half - 2 hours and I knew well where I was going. If you need extra time to figure out things (where/how to buy tickets, which train, where do I go when o get to Penn station, which NJ Transit train stops at EWR (vs. just Newark Penn, etc.)), if a flight is late, there are customs lines, etc., could easily be 4-5 hours between arrival and arriving at EWR to re-check bags. Let's not forgot crowds to navigate, particularly at Penn station, if arriving at the evening rush.

No way I would do this.