After entering in my net gambling winnings via your method listed above, my issue with the state return resolved itself. I most certainly have enough deductions to itemize and NJ thankfully counts gambling losses.
As for your final question, yes. The 1099-K sent by PayPal has total $ received for each month. Since I quit gambling by July, the few payments I received in the latter half of the year corroborate with the amount on my 1099-NEC. I guess if I don’t enter the 1099-K as above, then entering in the 1099-NEC wouldn’t result in that money being double taxed.
