Back to the original question, there are many boats out of Pt Pleasant, Brielle or even further north. A simple google search will get you 90% of them. They do range from "6-packs" (recreational & technical) to the larger boats like Gypsy Blood. My advice is to go out with a number of them until you find the one(s) that suit your temperament, diving style, etc.
And, as you well know, the boat "temperament and style" can vary from trip to trip as a function of who's running the charter. On Gypsy Blood there's a real difference between charters with "Shop A" vs "Shop B" and a "Gypsy Blood Open Boat." And even within each of those, there's often a difference between a trip to deeper/tech offshore stuff vs something more inshore well within recreational depths based on the types of dives and divers involved.