Ok, so I just typed a very long paragraph going in detail about how long a 60 person war would take (five people per team, which is what I think should be done). It turned out to be way too long (the paragraph), so I'll just sum it up. At the start of round six there should be a maximum of 576 cards (assuming everyone took no more than 30 into each battle). That's enough for one person from each team (assuming all twelve are still able to play). After that, the calculations get tricky, but I think it's safe to say that by round 9/10 there will only be two teams left with only one or two people in each. Since I was dividing the cards evenly each calculations, I'm not sure how that will effect the actual turnout (could be a couple more rounds, could be a couple less). Assuming there are 10 rounds, the war will take 36 days. So I would say the war should take anywhere from 30 to 45 days days depending on how things go and if we stick to SG's schedule. That seems perfect to me if we are supposed to have wars every couple of months. Oh, and I made it 300 cards per team to start instead of 240, since SG said she thought it was a good idea for there to be 60 cards per person.
In conclusion, can we make it five people per team instead? Yes, my calculations aren't exactly perfect for determining the number of rounds, but the total amount of cards at the start of round six should be less than or equal to 576, so up to that point my calculations are reliable (except that it's possible that some teams would already be out, and it's likely, too).
And about that spam, the times are so close together that it looks like it was on accident. It could have been a browser/internet error.