Yeah if you're not married to the whole drill out a mountain thing, the most "reasonable" answer is to go underground from a more workable surface location. Like a lot of the potash mines in Sask are in the range of 1100-1500m underground. Maybe repurposing an old potash mine shaft is the answer. You would have to go to Sask though... As mentioned above, terminal velocity is gonna be the real issue here for you.
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