The only attack I was thinking of when I wrote the Bitcoin header post, was all mining companies adopting tricks that give them some little advantage, but at the same time they degrade the performance of the network as a by-product. One of such attacks is cited when I posted about using approximate adders, and the danger that a monoculture of approximate ASICs can get stuck in a header that always generates a faulty addition.
Thinking out-of-the-box has both good and bad aspects:
+) on the positive side it allows novel and unusual solutions to enter the field, like your idea of intentionally breaking the topmost level in the carry-look-ahead login of a 32-bit parallel adder, which you called "approximate addition"
-) on the negative side it disconnects one from the already known solutions in the field. Some EDA tools already can split a 32-bit adder in a critical path into a pipelined pair of 16-bit parallel adders. The general methodology is called "register balancing" or "delay balancing".
You've made a far-reaching statements about a possibility or necessity of changing Bitcoin hashing algorithm in the face of your discovery. Have you consulted your discovery in private with somebody knowledgeable with digital logic design? What did they say?