I don't have specific experience with New Jersey, but the "don't pay" advice is rarely good when it comes to taxes.
First off, I would do some research on-line to see what constitutes a 'tax-worthy' purchase in New Jersey - some things may be exempt.
For example, here in Connecticut we have property tax on our vehicles. Except airplanes - for those we pay a flat rate depending upon the gross weight of the plane, not it's assessed value. To escape this tax on their cars, some people register them out-of-state. A vacation home in Vermont is a favorite ploy. As such, Connecticut will scan the motor-vehicle records in VT looking for CT mailing addresses (as opposed to a VT garage address). When I registered my dirt-bike in Vermont (required to ride on their trails), I got a call from the Connecticut tax-guy. Once I explained that it was an off-road vehicle (and I had since sold it), case was closed, no tax paid.
Another example of a sales-tax "oops!" is when a home-builder finishes completing their plane and registers it for the first time. That's when they're assessed a sales tax for the purchase of the kit... along with fines for the years a-building without paying. Seems the state expects people to pay a "Use Tax" (equivalent to a sales tax) on the purchase of the kit at the time the kit is purchased. As you can imagine, delays can add up.
You might get good results by simply calling the NJ state office and asking what taxes (if any) are due on a private airplane sale. You should be able to get some answers without having to reveal who you are. Note - get them in writing, as people's interpretation can be wrong. A pamphlet or web-site would be your best bet.
