Phantom, Hadestown, and King Kong have afternoon shows in addition to evening shows, so if it's possible for you to go to two shows, you could rush two shows in a day to really optimize the amount of time spent. I agree with Daniel about Ferryman, and the rush will probably be less competitive than Hadestown. I also really loved Ink, and that rush is online (on the TodayTix app) so you wouldn't have to wait in line at all.
If you're from New York or come to New York often, I'd say save Phantom/Chicago/Mockingbird for another time because they'll probably still be around after a year. Hadestown too probably, but it depends how much you want to see it sooner.
As far as King Kong goes, you shouldn’t have to worry about lining up. I went on a Friday evening in May, and got a solo rush ticket 2 hours before curtain. I paid 50$ and sat center orchestra maybe 5 rows from the stage. It was (in my opinion) one of the best seats in the house. They’re lucky if they pass 75% capacity, so I think they just sell 50$ tickets the day of, until the show starts in order to fill the seats... (not sure if the closing announcement changed things, but probably not.)
So I’d recommend doing an early morning lineup on a Wednesday for another show and then just make your way over to King Kong for the evening show.