I think it almost certain that you have a contract with Verizon that disclaims any liability for consequential damages in the event your phone malfunctions. Somewhere in a pile of paper you probably still have that fine-print contract which very likely binds you and prevents you from recovering for photos you lost. Also obliging you to pay what they charged you if you don't return the phone. See if you can find the contract, get out your magnifying glass, and have a look. Doubtless there is a warranty on the phone too; judging from what you say, they're honoring it.
Not legal advice as I don't practice law in New York or hold New York licensure. Consult New York counsel if you need legal advice. I practice in Vermont ONLY.
New York Courts do not take sentimental value into account when awarding damages. I think your best bet is to make every effort you can to recover the photos from the broken phone and then return the phone to Verizon as soon as possible.
Try to recover the photos, speak with a manager with Verizon to see if they will give you a limited time to return the phone due to the circumstances and request that the $500 fee be reversed.
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