Strongly agree with last post.
Depending how long it takes to get to the NJ Transit platform (due to AirTrain and purchase your ticket). If you boarded a NJT at 9:21pm (alt 9:00pm or 9:43pm) it would arrive NY Penn at 9:48pm. The next train leaving Penn would be 10:11 arriving Great Neck 10:46pm. There is a 9:48pm from Penn but too difficult to make it from NJT over to LIRR tracks with baggage within minutes but that earlier would arrive Great Neck at 10:23pm.
Due to location of Great Neck (North Shore) driving from EWR without traffic would take 1 hr (big assumption no traffic or construction/slow down)