How is it that concurrent miners do not subvert each other's work?
The number of hashes a miner has tried in the past does not affect the probability that a miner will get the correct hash in the next immediate calculation. Thus, it does not matter for the miner from an efficiency viewpoint if he starts work on a new block since the probability of getting the correct hash is exactly the same as if he kept working on the old block. 

Think of this coin flip example: The first goal is to try to get heads. You failed the first several flips and than the goal changes to getting tails. The probability of you meeting your goal is still exactly the same.