You're premise that miners can be expected to idle their machines when the reward halves is wrong.
With miners needing to sell most of 3600 new coins per day, the only thing that keeps the price of bitcoin even relatively stable at a given price point is a roughly equal rate of new money flowing in. When the price holds for a stretch you can bet the reason is that at least one whale feels the current price can be sustained by the incidental rate of incoming new money plus their own willingness to buy at that level. They view the need to buy mined bitcoin each day as an obligation, since failure to do so will cost them even more in terms of a falling price.
Anyone who's wrestled with the decision of how much more money to invest in Bitcoin to support the current price level should have realized that there's a balance to be struck between how many bitcoins are mined each day and how many bitcoins are purchased by new money each day.
The long price decline since Q4 2013 shows that bitcoin holders would rather be pushing $0.8M of new money into bitcoin each day than $4M (if the price were to go back to $1000). Think of it as the savings rate of the true bitcoin believers of which there are probably between 250,000 and 500,000 globally at the moment (
https://bitscan.com/bitnews/item/how-many-people-really-own-bitcoins-and-why-does-it-matter). Most of these people are limited in how much new money they can pump into bitcoin each day by their ability to earn non-bitcoin money each day.
Back to your premise: When the block reward halves, all other things remaining equal, you should expect the price to double. More specifically, if the price at the time of the halving truly reflects the savings rate of bitcoin holders, then the price should double.
Why? Because the savings rate is the sustainable rate of new money flowing in to buy mined bitcoins. The same amount of new money after the halving will buy half as many bitcoin at twice the price. Miners should just hold off selling until the price rises to that level. They should absolutely NOT turn off their equipment.
Of course when the price level is rising during a span of excessive exuberance, or falling due to a contagion of anxiety, what will determine the new price level once the dust settles is the new savings rate of the new/remaining pool of bitcoin holding believers.