Well, there are a few problems with your plan.
The first is that you can't use the GAD voucher to upgrade an existing ticket (the 3-day pass). What you can do is redeem your voucher for a one day ticket, then upgrade that one day ticket to however many days you need.
(Even if you could upgrade the 3-day to a 4-day, the cost difference between a 3-day and a 4-day is only $6 per ticket. It wouldn't give much value to the GAD voucher, even if you could do it.)
Since you have booked the QSDP, you are required to purchase tickets with your package. You can't book the dining plan unless you buy tickets (with a few exceptions that don't apply here).
So your choices are:
Downgrade your package to include one day tickets (if you are not within 45 days of check-in, you can do this at no charge). When you arrive, redeem your GAD voucher on your first day at the parks, then upgrade it to the number of tickets you will need. Your cost will be the ticket cost - the value of the GAD voucher ($79 per adult) + 6.5% tax. You will have one day tickets on your KTTW cards that will never expire if you don't use them. You can have them removed from your KTTW cards and you can save them for another trip. They can be upgraded when you return to the number of days you need.
If you don't want to have tickets to save for another trip, you can:
Redeem each voucher for a set of Fastpass cards for your group (up to six people) - this will give each person in your group a set of "instant" fastpasses for the park where you redeem the voucher. More info here:
http://www.oinc.net/disney/fastpass.php#gad
Or, you can redeem each voucher for the figurine and pin set, or you can donate the vouchers to participating organizations.
Alternatively, you can cancel the package with the QSDP and book room-only, then you don't have to buy tickets through a package and you can just upgrade the GAD vouchers to whatever you need.
Hope this makes some sense!
Edited to add:
I just re-read and see that you are going in May, so you probably have already made final payment. Disney may charge a $50 change fee if you change a package to one with a lower cost. Best to call and see if you can change from a 3-day to a one-day ticket if you want to save the tickets for another trip and upgrade the GAD (you can save the 3-day tickets as well and upgrade for another trip if you can't change the package, but I am trying to minimize your cost right now).
