I would never voluntarily fly from EWR if I was on LI. Definitely change to JFK (or LGA or ISP) if you can.

That said, LIRR to NJT isn’t that difficult and May be more predictable than driving. That said, to make a 10:15am flight you’ll probably want to leave 7 or 7:30 depending on where you’re coming from, and so you may miss the worst of the inbound traffic. I’d probably take the SS to Belt Parkway to Verrazano and across Staten Island, but may depend where in LI you’re coming from.