It's a great idea to store it in Manhattan as it's way more cheaper in comparison with the JFK storage (starting at 10$ in JFK vs. 2$ in Manhattan). But i would reconsider taking a cab downtown as you might get stuck in traffic and lose precious time. On your way back to JFK assuming you'll leave around 9pm you won't have that problem, as rush hour ends around 8 i believe.

I'm considering checking the carry-on so i won't have to worry about it, as i feel storing it will take too much time. I read the only storing facility in JFK is in T1, and i depart from T7. Might be faulty information though.