NJ does not automatically treat an LLC as an S-corp just because that status is granted at the federal level. Is it an option then to file as an S-corp federally, but file as a simple disregarded entity at the NJ state level?
No, it will not be disregarded.
The NJ division of taxation requires to explicitly request an S election, but not an entity election. The election to treat your LLC as a corporation filed with the IRS is automatically recognized by the State of New Jersey. The election to treat that corporation as an S-Corp - is not.
The tricky part is that when filing form 2553 for an LLC you're doing both: electing treatment as a corporation (skipping separately filing form 8832) and then electing treating that corporation as S-Corp.
So LLC electing to be treated as corporation with the IRS will also be electing to be treated as corporation with NJ. However, the election to be treated as S-Corp with the IRS needs to be reaffirmed with New Jersey using form CBT-2553, without which the NJ division of taxation will expect your filings to be as C-Corp.
You really don't want it to be handled differently at the Federal and State levels, it will be bookkeeping and reporting nightmare. Especially if you end up with a C-Corp at State and S-Corp at Federal.