I need the reverse of an alarm clock: A clock that somehow makes me sleep.
Because otherwise not only will my brain function worse, but the additional stress may actually shorten my life, which pretty much screws up the goal of getting more hours out of life!
Try setting the alarm for when you should sleep, instead of wake.
I need to do this myself, and reading your thoughts made it clearer to me. (Doubt I'll actually do it though...)
Meanwhile you can stop trying to be more productive. It is really overrated. Try taking a Saturday off and do nothing but read, watch good movies you have been putting off, and just relax overall.
Maybe I am abnormal here, but there is nothing in this world I could enjoy doing everyday for most of the day.