Note that the statute (2C:58-3 c(3)) says that a person with some kind of defect or disease must produce "a certificate of a medical doctor or psychiatrist licensed in New Jersey, or other satisfactory proof, that he is no longer suffering from that particular disability in such a manner that would interfere with or handicap him in the handling of firearms."
I have seen this interpreted as meaning that you need a letter from a physician, a doctor, such as a psychiatrist, NOT a psychologist. So it is very lucky to find a psychiatrist who will do this for $750. I would imagine though that Dr. Pirelli, who I believe is a psychologist and not a medical doctor, should probably count as "other satisfactory proof."
Here is the link NJgov link on how to vote Nov 3rd in NJ.
I think the safest method is: Hand the (properly completed mail-in) ballot directly to a poll worker at a polling place on Election Day.
Less chance of any funny business that way and it would not be a provisional ballot.
However, as intended there may be lines because of the reduced polling places open, plan accordingly.