@Arjen,
I ,at one time, was a very strong proponent of the existential nihilism you described, but I realized that it did not hold because of a simple fact:It leads to the question of wether we should even acknowledge logic, which, in the pattern of the reduction that has been followed to this question leads to a resounding NO! To utilize logic cannot be a matter of logic, only a faith in logic can dictate your utilization of logic because somthing cannot be based only in itself or it falls through. This line of thinking leads to a complete dissintegration of all certainty since there is no absolute truth and the technique of the reduction is one which cuts apart the shaky relative truths by exposing their lack of a base.
I am not sure of cosmic nihilism, but after the self-destructing logical reduction approach, it doesn't matter untill you make the realization that you are either dead or with faith in somthing even if it is logic, at which point you can move on. It may not be progress, but it gives a vehicle through which life is bareable and even enjoyable, it gives you a crutch, you might think, on which to lean your dogmatic frameworks. Life cannot exclude some dogmatism or it may as well be death but for the experience.