As long as you have the receipt showing that you dropped it off and they accepted it (they being the shipping company) - it is out of your hands. May have to call up Verizon for them to see this and make an exception so you don’t get a fee.
I used the Apple Upgrade Plan and got a receipt from FedEx when I dropped off my old phone. Took a day for movement, a day later, Apple received it and within a few hours, my return was accepted and old Citizens loan closed. So the whole return thing took about 3 days total including the day I dropped it off at around 5:00pm.
Hope you get this resolved. I was honestly super worried bout something like this happening when I returned my phone.