I've done some more calculations, and I've found that with four people per team, there will be a maximum of 1728 cards left at the start of the third round, assuming there are 60 cards per person when the war is started. If you have six people per team, there will be a maximum of 1728 cards left at the start of the fourth round. 1728 cards is enough for 57 thirty card decks, but only 144 cards per team assuming even distribution, which means 3 people per team can play. So, at the sacrifice of a single round, you could add two more people per team. If you wanted to add only one more person per team, the number wouldn't be the same after 3/4 rounds, but it would be about the same. Adding only one more round is only three more days. It's pretty clear that five or six people per team would hardly affect the length of the war.
It's probably possible to find the maximum and minimum amount of players that can play in each round (depending on how the cards are distributed), but I don't remember a single thing from calculus... 57 thirty card decks sounds high, but it's not because I highly doubt there would be more than 44 people able to play in the rounds I've discussed (give or take, I'm just guessing). With each following round, the number of people able to play decreases dramatically.
Oh, and I just recalculated the five people scenario, 2160 cards at the start of the third round, 1440 at the start of the fourth. No matter what, everyone will get to play at least two games (because there are 60 cards per person, but an exception would be if the team designed their vault poorly). After the second round, if your team did well, you'll have more people able to play, and if your team did poorly, you'll have less. All of that is for 4/5/6 players per team.
If your team loses all its matches in the first two rounds, you're out. If you win them all, you'll have 48/60/72 more cards than you started with in your vault, depending on how many people there are per team.
Anyway, I just thought some people might like to see the numbers. Again though, it wouldn't hurt at all to add one or two more people per team.