PAXboy has a really good idea. Creating the position of fatigue manager would be an entirely appropriate measure given the scale of the problem and the risk to passengers.
A fatigue manager could have terms of reference to manage fatigue in an holistic way. This would go way beyond simply assuming that compliance with CAP 371 prevents fatigue. Many issues could be considered.
However, just imagine the howls of objection from the airlines. A fatigue manager would put a break on the one issue that the airlines do want to resolve - production. Resolving fatigue issues ultimately means paying for more pilots.