I think the best solution to this has to be simple. All you really need is to find the perfect diamater hole to maximize the thrust of the built-up pressure. Of all the "tests" we did, the best results (e.g. farthest distance) occur when the cap of the bottle would be blown off, leaving the roughly one inch diamater opening as the thrust nozzle.
So to ensure the perfect launch, you will need to find a way to make the cap the weakest part of the bottle, so that it fails first. But at the same time it has to be strong enough to withstand the "normal" pressure of the built-up Diet Coke/Mentos reaction.
And as we also found, the body of the bottle itself will rupture sometimes before the cap would blow off. From these results you can conclude that if we had ever screwed on the cap of the bottle too tightly, then the bottle itself would break. But if the cap was not on very tightly - yet still on enough to keep the pressure contained - the bottle would blast off like a rocket.
So here's the challenge: to find a way to launch the bottle on a controllable launch angle, using this "cap tightness" observation.
