Aside from relying on any rush/lottery that they might announce in the coming weeks, my best advice would just be to keep a close eye on those specific dates. You never know when someone in the balcony might return their ticket, or something like that. Random tickets might pop up from time to time, I'd think. Keep a browser tab open when you can.
Also, I wonder what the re-sale landscape is gonna be like for this show. The show is selling well, but it's not booked solid, which makes me thing that the resale demand isn't going to be especially strong. In which case, it's worth keeping your eye on resale prices in the days leading up to your prospective performance, to see if the prices drop below face value. Or at least drop well below $350.