A couple of suggestions:

You mention your flight was "pushed back"; I am assuming this means your flight had a schedule change from the airline? Is there an earlier flight you could take on the same airline? If so call the airline and ask if they will move you to the earlier flight. Let them know that the reason you want to be moved to the earlier flight is due to their schedule change and they will likely accommodate you.

A quick Google online shows that PHX has a common Rental Car center: "The Rental Car Center accommodates all airport rental car companies, their rental counters and vehicles". If Hertz is closed there may be another company there still open and they are all in the same location.

If you can, choose seats near the front of the plane so you can get off quickly. You mention "we" so have the assigned driver sprint off the plane to catch the shuttle to the Rental Car Center while the rest of the group trails behind with the luggage or waits at the curb for pickup once the car is rented.