I understand your troubles it is close in distance but quite expensive cab ride and scheduled limo requires arrival at airport too far in advance.

Besides options given previously with Go28 to Newark Board St. for train. This can be tricky as there are two different flavors of Go28 and one doesn't stop at Nwk Board St.

Newark cabs have a flat rate so it cost $55 to drive a distance (to a town) even if short.
I'd suggest similar to previous response check the rate via S. Orange or Mapelwood based cab companies. It may be cheaper and if you can coordinate with them for your arrival so they pick you up at the airport (at departures) for slightly lower cost.

E.g. of above - last time I was too intoxicated to drive home from Manhattan late night I took PATH to Nwk Penn. The Newark company cab ride was a flat $55 but I called my townie cab company and they told me to wait at the Hilton for their arrival and it saved me $20.