Yes Funny Girl does standing room when sold out (which I think it usually is), though those tickets may also sell out fairly quickly. Make sure you allot enough time to get to the TKTS booth and then whichever theater you'll be going to as sometimes the booth may have a line (though hopefully it won't be long before show time), and you can use the app to check if the shows you're interested in have tickets there beforehand, as well as the price range of available tickets.
Hadestown is on TDF for that performance, so it stands to reason you could probably get a decently priced ticket. Definitely enter the lottery through Lucky Seat, and you'll know the day before or so if you've won (though be warned that seats could potentially be partial view). If TKTS doesn't have anything you'd want sometimes the box office will take off premium pricing right before a show, so it doesn't hurt to check there as well (or if it's super close to a show, sometimes resale tickets will actually be below face value, just make sure they're instant transfer).
Leopoldstadt does in person rush as well as lottery (through rush.telecharge.com), and I feel like your chances of scoring a rush ticket for the matinee shouldn't be terrible, so you can always give that a shot too if you feel like it.