Final question -- do large mining operations network their miners so that they don't overlap their hashes.

There is no need to do it -- if each miner has a source of true randomness, then it's enough that each miner randoms large number (how large, depends on the number of miners, see the birthday paradox), and slap it on to "salt" their block. If the number space is large enough, it is unlikely that two different miners will get the same salt.