I just called the Nassau County Board of Elections and surprisingly got through to someone helpful right away. She was able to confirm my ballot style and that it contained choices for many district numbers that I was not aware of: court district, assembly district, senate district, etc. It was in fact a ballot-on-demand printed especially for me. Sorry for raising this false alarm.
No worries! It’s the close (and early) attention of folks like you that will make this election run better, whatever the outcome. Thanks for letting us know how it worked out.