Is this Othello particular geared toward students? And how young are you expecting these audience members to be?
Unless it is a particularly approachable version, wouldn't most students attending Othello in particular be high school students? Teenagers naturally stay up later - no matter what time school starts in the morning.
And frankly, the trek to the Delacorte is always a pain whether your train is running or not. I, too, would prefer an early curtain, but it really is a personal preference.
That being said, the Public is doing plenty make sure Shakespeare is accessible including borough distribution and the mobile unit. And the more approachable of the two shows for young people not familiar with Shakespeare is smack dab in the middle of NYC public school summer.