Other Options are:
1) Try to gamble and see if any sleep rooms are available at AS. It is first come first served, so no guarantees.
2) if that fails, try to sleep in family room at AS. Usually people are quiet.
3) If you are not price sensitive; just spend the money and just book the Oryx transit hotel to get guaranteed sleep and shower. Come back to AS for breakfast.

Personally I would do number 3 to get guaranteed sleep versus potentially wasting time with one or two.