Thanks for all the help, guys.
Updating incase someone in the future finds this in a similar situation and it helps.
The flight to Tampa at 4PM was OK, departure from the gate was on time, airborne about 30 minutes late due to de-icing. One good thing: no lines at the airport. lol
My best guess judging by what I saw in JFK is that indeed flights that had to LAND in NY were cancelled while flights where the plane was already there went out as planned, which is about 10% of flights (my guestimate).
50 mins before the flight after spending some time at the terminal and getting confident that it's gonna be ok (staff seemed to confirm, other departures were on time, etc) made a call to Mears and booked an SUV to our Disney World resort.
It cost just about what a flight what would cost, but it made sense as it ended up about 1 hour 15mins and with 2 babies after two crazy days, we wanted the most comfort - didn't make sense to wait for another flight + baggage claim + Disney shuttle.
Also considering this is a long anticipated vacation, an expensive one, incl trans-atlantic flights, $400 (icl. tip, tax & car seats) was well within our "unexpected" budget column.
The service wasn't the best, wouldn't recommend if you have time to research - we had to install their car seats ourselves, the driver had no idea how to. Other than that, easy comfortable ride and the nightmare was behind us.