If the majority of bitcoin-exchange market supply is coming from mining, which currently seems to be the case,
Not at all. Not even if we assume miners selling every coin they mine.
Source: blockchain.info
and that supply halves, that's a supply shock. If demand remains the same, the price must roughly double.
A fundamental misunderstanding of how the market works.
If that was really the case, GM could simply cut the number of cars manufactured in half, and double the price. Profit!
If there were only 100 cars in existence and there would never be any more, then we destroyed 50 of them , yes, the price of the remaining cars would skyrocket...