Hmm, this 32 bit signed integer must be greater or equal to the current block version. Plenty of space here. Discussed on github: No forking Extra nonce added to Bitcoin header
I believe Danny's point was that it invalidated the midstate to change it.
If there exist some algebraic attack that breaks two rounds of SHA256 (and OP is hunting for it with statistics), it's quite possible that the variant of such attack will bypass midstate and break 3 rounds, from 640 bit header to nonce. So the next suspicious thing are unusual block versions in the blockchain.