Quick report from my trip. My wife and I flew up to NYC just to see Hamilton. Took a taxi directly to the cancellation line from the airport on Tuesday and we were the 9th and 10th people in line at 1:00 PM. We got tickets at about 6:15. There were a LOT of tickets that day, probably 25 or so, sold to the cancellation line. People who got in line at 5:45 for the 7:00 show ended up getting in.
Saw Javier as Hamilton.
So the next day we happened to be in the area trying to figure out what matinee to go see and we saw that there were about 20 people in the cancellation line and figured "what the hell, let's wait". So we waited and ended up getting the last two tickets (actual cancelled tickets) just a few minutes after 2:00.
Saw Michael as Hamilton.
Definitely spent more money than anticipated, but the show was amazing both times and it exceeded every expectation we had. So, if you can get there on a weekday I think you're likely to have better chances as there were at least 20+ tickets sold to the cancellation line on both Tuesday and Wed. matinee. Though this was also the first two shows after Chris Jackson left, so any VIPs who wanted to see him came last week - which is likely why they had so many tickets for these performances.