I'm no expert but I know there is a limit on the # of forms of payment you can use on SW. So, for example, don't buy 8 gift cards thinking you can apply them all to your single purchase. (I want to say the limit is 4.)
I used gift cards a few years ago and there was a limit on number of gift cards, so, I ended up booking each person separately. It ended up being a major pain at the online check in time, there were 6 in our party though, it may not be as much of a hassle for you
I just did this a few weeks ago and it worked out fine. I ended up having to book 3 members of my family and then immediately booked the other 2 family members since there was a limit on how many cards you could use at once. Other than that, it was easy. The savings was worth it.