Thinking harder I guess the only reason that mining difficulty is so competitive is that there's a reward for mining, given to just the miner, so the arms race is profitable (much as, say, the arms race for microsecond-level tech improvements is profitable to HFT because even if two algorithms make the same decision only one gets the purchase in first).

So if you get rid of that, and maybe add a nominal "reward" for solving the puzzles to remain in the network and give it to all participants, the incentive to build giant mining farms goes away: the only reason to have additional computational power is either to keep up with the network as a whole (not the fastest person in the network) or to actually gain 50% of computational power.