The librarian queried the Chair of the NYC Councils Committee on Government Operations shortly after this question was posed in February, and did not hear back. He also hit dead ends with Fordham Law School and NYPL's Science, Industry, and Business Library.

Here is what he came up with 6 months later:
As noted in the cited section, local governments are given autonomy from the state: IX, 1 (b) "All officers of every local government whose election or appointment is not provided for by this constitution shall be elected by the people of the local government, or of some division thereof, or appointed by such officers of the local government as may be provided by law," and the Hme Rule act of 1964 specifically states in section 51 that is subject to liberal interpretation; that is, municipal governments may act on the assumption of rights within their jurisdiction and it would be on the state to challenge any such actions.

However, Article VI, section 15 of the State Constitution deals specifically with the creation of the judiciary within the City of New York, by act of the (state) legislature. "§ 15. a. The legislature shall by law establish a single court of city-wide civil jurisdiction and a single court of city-wide criminal jurisdiction in and for the city of New York..."

So, the creation of the judiciary seems to be reserved to the state legislature, and by that interpretation such a tribunal as the question proposes would require an enabling act of the state legislature.

The text of the NY State Constitution can be found here: http://www.senate.state.ny.us/lbdcinfo/senconstitution.html

This interpretation should be vetted by a legal expert familiar with NY/NYC administrative codes before being considered a definitive answer.