Thanksgiving is another crazy time and the show didn't sell out then... usually, your best bet is to go play their lottery and, if you lose, they usually offer lottery loser seats for only $10 more.
I'd just ask if they would be offering lottery loser seats, and if so, go for it.
If you win, I'd just let other winners line up before you, so that you're last, and then say you won two/four tickets, and need three/one lottery loser tickets, too, and they should be able to put you all together, or at least break you up in two groups with an adult in each.
If you rather TKTS, that would free you up to not be hanging out and killing time for lotteries and such when you could be doing other things...