RE: West Point, NY
I have not bow hunted at West Point so you should check the rules for that season.
As far as the checking/out rules. During the gun season you had to sign in (returning - when you are done hunting) no later than about 17:30 (5:30pm). They post the sign in time each day based on about 1 hour past sundown.
They told me if you can't get the deer out and to the check station by sign in time , you should leave the deer and go and sign in and explain to the MP's that you need to go back and get your deer. The problem with that is you have to return the next day to have your deer checked in.
If you are late(after sign in time) returning to the range control station, they will send out MP's to look for you.