Following up with what happened with my ticket: I went to the court about 30 minutes early, and was able to sit through a set of folks that were being called in a group prior to mine. This is how it proceeded:
The Judge and a Town prosecutor were the primaries. The Judge would read out what the violation was for each person. The Prosecutor would let the Judge know if there were any priors, and what if any plea deal/reduction he was offering. There would be a little bit of discussion between them, and the Judge would reiterate the deal to the person, and ask if they wanted to plead guilty to that.
I found that the more priors someone had, the less of a reduction the Prosecutor was willing to give. And in a couple of cases no reduction was offered. It was all pretty consistent with the amount of priors and degree of speeding/etc.
For me, they offered a reduction to a Stop/Park violation - Parking on a street where it is not allowed. I accepted and pleaded guilty. My fine was $150 plus a $25 surcharge.