>>1031008I recommend don't custom build a bike with only one ride in mind. On a bike dedicated to climbing on the road, why would you only have one speed and no rear brake? Why a mountain bike frame?
Any road bike will do. Saving 3lbs. of shifters and cables by building what you described does not make much sense to me.
What is the elevation and grade of the hill you have in mind? Do you have friends/family to support you?