if you are so desperate then pay up the extra night before.

If you are flying Business/First you could use the lounge on arrival (I assume you are not, otherwise you would sleep on the plane).

If you have lounge access (paid) such as CO, NW or DL you could use the lounge when you arrive.

The other option is talk to your doctor and have her/him give you some sleeping pill, have dinner before you board and then sleep for most of the flight.

And by the way, the worse you can do for jetlag is go to sleep at 11 am. Stay up, get some sunlight, maybe have a short nap or just go to sleep at 8 pm and wake up early the next day.