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In terms of the issue of falsification, it seems that Kuhn's primary rejection of falsification is that a theory cannot in fact be made untrue, but rather it becomes no longer useful. I don't think he would argue that there is no room for the kind of falsification you are describing. That is, a kind of methodology that works to challenge and criticize the current paradigm, once a flaw has been found. An important question seems to be: what is the qualitative difference between the practice of falsification of normal science and the practice of Kuhnian normal science? The applicable usefulness in the moment of the practice seems to be the most distinguishing characteristic between the two practices. However, that does not mean that the idea behind falsification, the idea of challenge, is not a part of Kuhn's scientific model, it may just be that it comes about in a different way -- through the recognition of an anomaly, which occurs through the practice of using science in its capacity to help us, not in a search for a metaphysical or essential truth.
Kuhn rejects the idea that a theory can become an untruth, and therefore, he might ask where falsifation gets us. A paradigm which is left behind for a more useful one is not false, it is only no longer as helpful. I think he is trying to to save us from perpetual schizophrenia about what is myth and what is true. If we allow for paradigms that were once true to be falsified, we allow that all that we believe to be true could in fact be myth at any moment. Can we actually live this way? And a more Kuhnian question, would it be fruitful to live this way?
So, falsification would seem to be this force that allows for paradigm recreation and challenge, without allowing for the possibility of destruction and unstable skepticism. So that incomensurability, as you say above, "would be understood not as a permanent state but rather as the incentive that drives still broader paradigms within which existing ones can be compared (without, however, ever mentioning "reality" in any absolute sense)."
Whether or not there is an objective world, science should be useful! Therefore teaching to use science, by training to both challenge the truths it claims as incomplete and to give a basic foundation from which to work are important. Beyond all of this, I believe in a model of education that works to help students develop the tools that will enable them to become active participants in a world. To learn the skills to deconstruct assumptions and establish her own imaginative possibility to perceive herself, her community and her world in changing and exciting ways. Science education should be a part of this process of self and world creation, but this also means the educative experience cannot disregard the current truth that her community operates under.