Red Zone changed my life. I have problems watching a full NFL now game unless I have money on it or there's some fantasy implications. ...but I would try to pull the all-nighter.
you could slot the start times 1:30 apart
have both conferences play around the clock
the only start times locked in are the 2 worst teams in each conference per draft Browns vs Jags SF vs Bears 3 am and 4:30
the best 7 teams pick the start times they want so NE picks 1st