LV 51 Cornfield Point - Can't seem to find a 4 word name. It was also at Sandy hook so would have carried that name.
I was hunting through this list http://www.uscg.mil/History/weblightships/LightshipIndex.asp and had gotten as far as #51, but would never have gotten the answer without all the final clues. I was leaning towards LV 1 : Nantucket New South Shoal but couldn't find an experiment on the vessel. Though I guess since it was #1, the whole thing was an experiment.
Coast Guard information on LV51: http://www.uscg.mil/History/weblightships/LV51.asp