And 5 of those top 10 are all in one NJ county - Hudson County.

The people at the polling place absolutely should have given you a provisional ballot, as u/Aromatic_hamster said.

I had this happen about 35 years ago. A neighbor had reported that I moved out of the district. I was away at the police academy. Nosy neighbors can suck sometimes.

But, thankfully the folks working at my polling place knew me well enough, and did the right thing by offering me the provisional ballot and explaining the next steps.

I would complain to your local board of elections about this.
See if you can find out why you were removed, and register your displeasure with the people who did not help you.
You have the right to have your vote counted.

If you have time and the stomach for it, you can still go back there now and ask for a provisional ballot.

As u/spiritfiend pointed out, make sure you are going to the correct polling place. A lot of us have new locations to vote at.

Upper Saddle River closes today https://www.usrpd.net/wp-content/uploads/2022/10/Job-Posting-Upper-Saddle-River.pdf

Department Of the Interior - Park Police https://www.usajobs.gov/Search/Results?j=0083&d=IN&hp=public&p=1

Rutgers University Police Department https://ipo.rutgers.edu/publicsafety/rupd-recruitment

Go local.
The big sites that list lots of jobs can be nice, but actually looking at each department can also be helpful.

In Hudson County, the Prosecutor's Office doesn't hire from civil service lists, and I don't think Secaucus PD does either.
If you can get into any department in a civilian position, that may help your application later on, too.