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You can do it if things fall into place perfectly. Let's look at your time frame:
Arrive at 12noon check/store bags for later flight, taxi/public transportation to Battery Park/Castle Clinton, get there around 2pm, purchase ferry tickets, wait in line for the ferry (best to book tickets online! www.statuecruises.com) which stops at the Statue first and then Ellis Island. Depending on what time you catch the ferry will dictate how much time you will have to spend there. Last ferry leaves Statue at 6pm. Return trip to JFK to arrive by 8pm or thereabouts. Check with Virgin Atlantic when the earliest you can check bags. There's luggage storage facilities in terminals 1,4,8. Taxi will be fastest to/from JFK.