I think your big question to answer for yourself is what are your larger goals and how does what you have with stony Brook help get you there? An Ivy League phd does not guarantee you a job, nor does a SUNY degree bar you from employment. The Ivy League will of course open more doors for you, but that only mean that you get maybe some consideration that others may not. That does not mean you are guaranteed anything, it's still up to you to secure the job.
The other question is, if you have a JD already, why are you even bothering with academia?