Basically, the idea is to put in the first 64 bytes a 4 byte hash of the second 64-byte chunk. That design also allows increased nonce space in the first 64 bytes.
But it you want to do a simpler change, you can more easily use the first 32 bits of the Parent Block Hash (now currently zero) to store the first 4 bytes of the SHA256 of the last 16 bytes of the header. That way to "tie" the two header chunks. It's a minimal change (but a hard-fork)
But some ASIC companies already have cores that are better (on power, cost, rate, temperature, etc.) than competing companies ASICs. Why do you think a 10% improvement from AsicBoost is different from many of other improvements they already have (secretly) added? Maybe we (?) should only allow ASICs that have a 100% open source designs?
If we change the protocol then the message to the ecosystem is that ASIC optimizations should be kept secret. It is fair to change the protocol because we don't like that certain ASIC manufacturer has better chips, if the chips are sold in the market and anyone can buy them? And what about using approximate adders (30% improvement), or dual rail asynchronous adders (also more than 10% improvement) ? How do we repair those?
Disclaimer: I have stake in AsicBoost, but I'm not sure about this.