Does the model take into account your 6 month old baby or your loud neighbors?
The solution is easy. Pay a much lower basic salary but pay a !!!! load in flight pay and leave it up to the pilots to decide if they are safe to fly. And allow pilots to call in sick or fatigued whenever they please, with no penalties or requirements for evidence.
The problem right now is that the basic pay + 60/70 hours vs 90 hours is not enough of a difference for guys to really care about the extra 20/30 hours vs. the extra time off. Its called opportunity cost, how much do you value your free time vs. extra flight pay? Once you've bagged around 70 hours the extra 20 isn't worth the flight pay over the rest, the rest if more important. A really high flight pay would make guys think hard if they are fatigued, but at the same time would mean that guys who really do need the rest would actually call in fatigued or tired or whatever.
Added to this would be serious consequences for guys who show up for work in an unacceptable state for the pay. Once the culture of knowing when to call fatigued is understood the company will be confident that their pilots are not kidding around when they call in fatigued or tired, because not flying will become a lot more expensive for the pilots. At the same time with the policy of taking a guy at his word there's no excuse if a guy shows up in a condition unfit to fly an aeroplane, penalties should be harsh and rightly so.
It would work. The work force will police itself and the company can throw away their fatigue reporting system. After a while the company will easily be able to identify how many hours its pilots are willing to fly, and see trends in pilots reporting fatigued. Rosters can be adjusted accordingly.