The consensus is NYP has overshot it's capacity: https://www.youtube.com/watch?v=h5XsTmzfqDs The time is long past for serious consideration as to why all of NJT and LIRR commuters must go to NYP. Diverting some LIRR trains to GCT will help. Even so, New York is of sufficient size to warrant a third major rail depot.
LIRR has some options,but you need to change to the Subway to cross under the East River.
ESA is still some what behind the "eight ball" construction wise,Hunterspoint Ave is a 2 track station,a quick connection to the #7 subway
is possible,but that's "overloaded" as well into Times Square.
The old ferry connection at Long Island City is long gone,and has limited amount of 3rd rail equiped tracks,and also feeds into
the "overloaded" #7 into Midtown Manhattan
"Alantic Terminal"(aka,Flatbush Ave) is possible for those that work in lower Manhattan,there you can connect to 9 different
Subway lines(B,D,N,Q,R,2,3,4,and 5),but is somewhat strangled for equipment storage trackage.