I'm not thrilled with who I got my nuc from because they weren't all that helpful when I questioned this queen weeks ago. I'd have to contact another local beek and hope is not to late in the season 1. To requeen 2. To build up enough to survive the winter.
I know your "season" in NJ is MUCH Different than what we have in Louisiana. That being said, it's not even July yet, I'd have to think if you requeened ASAP they'd have a decent chance. Considering it's your only hive, I don't see where you really have any other options.
I know this advice comes late, but this is really why a "one hive" start up approach has a lot of disadvantages.
Your only other option is to try to get another hive, Nuc, or swarm and do a combine or shake out. Or donate them to a local Beek to either combine or shake them out. One thing is pretty obvious...they have no chance on the path they are currently on.
Personally, I'd requeen...think of it as a $20 lottery ticket. :)