Is it possible to mitigate this effects by establishing the rule that, when the block chain forks and there are 2 blocks at the same block height, miners always choose the block with the lowest hash (both blocks would obviously have hash below the target).
This is an oft repeated suggestion going back to at least 2011. It opens a trivial attack where when you do get a very low hash you refrain from announcing it, comfortable in the fact that you're guaranteed to win a race should one arise. In doing so, your competition is all wasting their time mining along a path that is likely to lose. The effect is stronger the larger you are, creating an increase in expectation for larger miners that doesn't otherwise exist.