Here’s a few 5pm shows that are on the books for the fall/winter as well as some other weird showtimes. I’ve been trying to do a 4 show day myself on my next trip so I’ve been doing some research.
Phantom does 5pm shows on Sunday’s.
I know not broadway but the Rockettes do 5pm shows quite regularly and 10am/pm shows as well.
And Mike Birbiglia’s Old Man & The Pool has 4pm shows a few times during the run (mostly on Saturdays). During its run (mostly on Saturdays). If you do a 90 minute show at 2, you can easily make it to Lincoln Center from most theatres on broadway.