Apparently TalkOrigins either didn't consider the hibernation option or they rejected it outright.
In all likelihood, God saw to it that only a manageable amount of animals were awake at any one time. Thus not over-burdening the crew in the sanitation effort.
As for having to carry waste up flights of stairs, that would not be necessary either.
A simple rope and pulley system could be used to hoist the waste to the surface and have it dumped over-board.