Okay, nope... it was DEFINITELY white-listed then. It shows up as an iPhone 6 plus on the Verizon site. They told me that they added the IMEI to their system. I hesitated to mention that Verizon stores have SIM cards, because my understanding is that you have to go in and *purchase* a new SIM from the brick & mortar store for twenty bucks, while the customer care team actually just sent one to us for free. Plus, after the BS I had to deal with from the physical store earlier, I wasn't inclined to go back lest I risk losing my **** on idiot sales people. The problems all stemmed from sales people in the stores being on commission, and they simply don't care to do crap for you if you aren't buying new phones.
If you can step into a store, buy a SIM; then go home and activate the service with the new SIM in your existing device, you'd speed up the process immensely and have a Verizon activated phone by the end of the day. ONE SMALL PROBLEM-- I'm uncertain if the 5s is compatible with Verizon. There's an IMEI compatibility tool on the Verizon site, you'd have to do that first.
ETA: I wasn't actually IN a Verizon store when I called customer care, I had to wait until we got home. I would have done, just to mess with the ****** sales clerk, but we had manfriend's kids with us.