Update on my chat with Corporate.
First, they are only going on a case by case basis. If someone wants to argue the payoff/buyout, they need to contact Corporate and talk it out Leadership | About Verizon . The reason they aren't offering this as a global sort of offer is just due to the number of customers and the manpower that would be required to implement everything; as a project manager and business analyst, I'll keep my view on that to people's imaginations 
to keep from possibly burning good will bridges.
Now, a few things. There are two types of contracts; 24 months of payments and 100% cost, or 24 months worth of payments and 50% cost to get an upgrade (the previous annual upgrade option). Either way, the phone, whichever one the customer has, MUST be fully paid before they can upgrade. What this means is that if a person had the 25/50%, they still have to pay the 12 month balance on the phone (the equivalent of the last 12 payments); they would just be allowed to upgrade once the phone was paid to the 50% value. I admit this didn't make a whole bunch of sense, as, the customer could upgrade at any time once the phone is paid off, regardless of when, the way current contracting goes. A customer could make three payments, pay off the balance and immediately upgrade.
The offer I was given was this. My payment agreement was for 24/100% (I was never given an alternate possibility). I will have my 12th payment completed on 15 September, at which time, Verizon would credit exactly half of the amount owed, so, by numbers, $214.50 to apply to the phone balance, leaving a cost of $214.50 to pay in order to do the upgrade. The other option was to, before my next statement comes out, credit the $214.50 to my account balance, which, with my bill would mean no payment required for the month, with balance applied to the next statement. It wouldn't be applied to the balance on the phone, but the idea would be to reduce the bill to save the money to get the half credit to pay off the phone. Same end result, just applied differently. There is no 100% buyout being offered even with corporate contact. This is a one-time ever option and wouldn't be offered again. So, if someone says, I don't like the Note 8 I want to upgrade to the Note 9, they would have to have the phone fully paid; no reductions or credits.
The current promotion is as written. The $480 cost reduction over the course of the standard 24 month payment agreement. If someone wants to buy the Note 8 outright, or they want to buyout the overall cost early, they would not receive any reduction in the cost, or would not be credited the remaining balance of the credit, as currently offered. A trade-in would still be allowed obviously but it is reduced to the regular trade-in value and not the promotional, 24 month payment plan, credit. I've never done a trade-in as my previous phones have been given to family or friends; is the amount an immediate credit and reduction or is it applied over time..like the credit currently being offered over the 24 payments?
Verizon did indicate that it is possible (not guaranteed) a different promotion would be given once the pre-order time ends on 14 September. Starting 15 September, the phones will be available in the regular stores...obviously available inventory depends upon the individual store location.
Next, for the heck of it I ran the process through Verizon online. When I requested the option of the upgrade, I was given two choices...either add the new device (as a second line) or pay off, in my case the Edge, and keep it; there was no option for payoff/buyout and trade-in. I added it to the cart anyway, under the payoff and keep, figuring I could go through the regular trade-in process at the end..nope, the Edge did not come up as a trade-in option; only my iPad and funny enough, the Note 7 (sent back last year but still showing as an inactive line). I asked about this, and Verizon indicated a pre-order with a remaining balance on the payment plan is not possible in one transaction. The customer would have to first pay off the phone in one transaction, and then go through the pre-order process. I am guessing this also holds true for any orders placed after the pre-order period.
I admit I forgot to ask about the Samsung deal and moving it to Verizon; if the Edge could be paid off with extra payments or if it had to be maintained as a new line alongside the Note 8. If I get some time I'll call back and see if I can get that question answered.
Hope this helps