They can solve this without a new battery type, I think, via the battery grip.

Make it so that when you're using the grip you can choose between two modes: Extended Life, or More Power. Extended Life, is how it works now. I'm not sure if both batteries are used in parallel, sipping power from each, or with the second used as a backup when the first one dies. The More Power mode would use both simultaneously, but rather than sipping, it would use the full power to drive faster AF.

Maybe the camera would decide on the mode on the fly, sipping from both, and then when doing AF it gulps from both. Perhaps the grip already does this, but Canon doesn't advertise it.