The New Jersey Driver's Manual states that a motor vehicle windshield should not have chips or cracks in it. It should always be clean inside and out. Always make sure windshield wipers are working. New Jersey law prohibits most drivers from adding tint to windshields and front-side windows.
New Jersey title 39 subsection 3-75 (39:3-75) discusses windshield and safety glass. Here it states that among other things that the term "windshield" shall be construed to include wings, deflectors and side shields; also front corner lights adjoining windshields.
The law goes on to say that no person shall drive any motor vehicle equipped with safety glazing material which causes undue or unsafe distortion of visibility or equipped with unduly fractured, discolored or deteriorated safety glazing material, and the director may revoke the registration of any such vehicle.
Since the law appears to us to be a bit ambiguous it would seem that a law enforcement officer would be the judge of if where the crack is in a windshield would be unsafe and warrant a ticket or not. You may try contacting a local police station or the NJ MVC to see what the normal stance is by law enforcement regarding a crack that is on the passenger side of your windshield and if you could be cited or given an "equipment" ticket for this.
You mentioned the inspection process in NJ. From information we have found under a New Jersey Motor Vehicle Commission plan, a cracked windshield, inaudible horn, broken wiper blade and 15 other defects only rate an "advisory." This means a simple warning to get it fixed, but no return visit. They did not state that the cracked windshield for inspection only would need to be on the driver's side to cause a repair to be made.
So now upon completing inspection in New Jersey motorists receive a handout from an inspector listing any advisory conditions that must be repaired. Motorists will then have 60 days from the date of the inspection to make those repairs. If not, the motorist may be cited for failure to make repairs and be subject to penalties. Motorists do not have to re-inspect their vehicles for advisory items. At any time, though, a vehicle may be cited for equipment out of compliance.
If you have comprehensive coverage you can make a claim for your windshield and get it replaced this way, minus the deductible you have chosen for this physical damage coverage.