Let your local Democratic Committee know about the proposed rule changes!
Chances are, most of your local Democratic Committee members are not familiar with the rules of the NYS Democratic Party, but once they hear about this issue they will likely want to sign the petition. They may even want vote to endorse the proposed rule changes as a committee. Here's a sample resolution they could pass. If your local committee does pass a resolution, ask your local Chair to contact the proposers of the rule changes so that the committee's name can be added to a list of endorsing committees.
If you're not familiar with your local Democratic Committee, your best bet is to search online using your County, Town, or City name, and "Democratic Committee" or "Democratic Club." With a little poking around, you should be able to find them. If that doesn't work, call your County's Board of Elections and ask the Democratic Commissioner how to find your local committee.