Could not date and variety ID your first NJ copper find but this one I am 99.9% certain I have nailed down not just the year but the variety. After comparing your photo with the NJ plates and seeing that the shield side had a feature not found on too many varieties I came to the conclusion your 2nd NJ copper is not Shot, it was identifiable and it is a 1787 Maris 6-D variety, Rarity 1, Very Common.
Redbook is nice to look at but not good at all for true ID of a type of variety, There is a plate chart on the Notre Dame site showing all the varieties and by comparing with the photos a possible ID is to be found if enough details show.
The closeness of the word UNUM to the shield and the orientation with the pales in the shield are what caught my eye. I did put in the photo a Maris 54-k variety which is the Serpent head type, and they are a Scarce variety and many detectorists think they found a Serpent head type when for the majority it is something else, usually a Very Common Maris 43-d variety.
I do think the 1st NJ you found may also be a Maris 6-D but without any of the letters showing in the photo, no way of saying, but the shield shape is similar....
Thanks for providing the county and state for my survey, now up to 430 coins and counting in it...........
Don