If you're going to be anywhere near Penn Station, and don't want to store your bags at JFK T1 or T4, I would try storing them with Amtrak. If you are asked to produce a ticket, you can buy a cheap NJ Transit ticket to Newark Penn Station from nearby ticket machines. Ask the Amtrak baggage attendant if a half-fare senior citizen ticket would suffice (even if you aren't a senior). After all, you won't actually be using the ticket.