I purchased my Note7 through Verizon's website. I spoke with someone in Customer Service last night and he said I had to go to a Corporate Store where they would issue me an S7 and then when the new Note7s come in, I could go back to that Corporate Store to exchange the S7 for the new Note7.
I called one of the local Corporate Stores today and the manager that answered told me the same thing as above. I went to the store and everything went pretty smoothly. I was hoping to get an S7 Edge, but they were out, so I got an S7. The lady that helped me made notes in my record that I wanted to come back and get a Note7 and they even took my name/number down to call me when they finally get the Note7s in stock (that's what the manager there wanted to do - don't know how many other managers will do that). They won't be able to place a hold on a new phone for me, but at least I won't have to call them every single day (maybe just once per week). We'll see how this ends up working out, but at least I have a different temporary phone.
To find a Corporate Store near you, scroll to the bottom of the screen and click Store Locator. Type in your location and check the box that says "Do not include Authorized Retailer."
