What Would Happen?

Right now it looks like the New York Giants are going to seal up home-field advantage throughout the NFC playoffs.
If that happens, they'd need to win one playoff game in order to host the NFC title game at the Meadowlands.
And as it stands right now, the New York Jets are in a great position to win the AFC East, and if they can somehow pass the Steelers (or beat them in the playoffs), they could host the AFC Championship game if the Titans get knocked out before then.
A lot needs to happen but just for the sake of discussion, what would the NFL do if both conference title games were to be played at the same stadium?
They can't force one team to give up homefield, not even to the extent of them using another field in New York (not that there is one). I don't think they could move one of the games to Saturday.
I think if this happens (unlikely though it may be), they would have to play one game at 1 pm and the other game at 8 pm. It would sure make for an interesting situation in the parking lot at around 4:30.