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!