One time, while upgrading a Macbook, the local Apple store simply could not process my trade-in. They simply couldn't and wouldn't accept my Macbook even though I selected trade-in at time of purchase -- which Apple could see in their order system. So the Apple store employees called into Apple trade-in HQ and had them start a brand new mail trade-in, i.e. the process of shipping to me the trade-in box for the usual mail trade-in. That worked fine and my rebate was credited within two weeks.
I tell you this for the following reason. If your local Apple store, for any reason, is unwilling or unable to process your in-person iPhone trade in, see if they will do this for you. See if the Apple retail employee helping you will initiate a mail trade-in of your iPhone by processing the request directly with Apple. You'll get the trade-in box quickly and will likely have your rebate within two weeks, and probably within ten days from the time you mail it in. Apple's agents process shipped trade-ins very quickly.