Boycotts almost never work even when the boycotters have other options... Like choosing one restaurant over another. Virtually no one is going to give up a hunting season with no reasonable alternative choice.
Besides that, hunting licenses long ago got stupid expensive, 10s of thousands of us bought lifetime licenses before the last price increase. We can't boycott even if we wanted to.
Letters DO work, as do phone calls. Obviously not every time, the dedicated antis aren't changing their minds any more than you or I. It's the fence-sitters that listen to reason.
Moving can be a viable option when the state is failed beyond reason, which definately includes NY. I'm leaving, ASAP, and encouraging as many others as possible to follow.