Not sure what you mean by this: " ...hay has the most respiration (amount of time to loose moisture..."

Respiration is the process down at the cellular level which converts stored sugars into energy and CO2, so that the plant can live.  Just like people do.  Respiration will continue to occur, until the plant is shut down.  The goal is to shut down the plant as quickly as possible.

Regarding the debate of whether to mow in the morning, in the evening, or at night........ it depends on where you live.  If you live in the humid East Coast, you want as many hours of sunlight as you can possibly get to dry the hay out as quickly as possible.  If you live in the arid West, you can wilt hay quickly by low humidity, so mowing late in the afternoon or even at night can work. 

What works *here* may not work *there*, and what works *there* may not work *here*.

At least that is the way I see it.