You suggest that knowing one's death date would compel a more urgent questioning of what is worthy of our fervor — but I want to press on a prior assumption buried here: whose fervor, and which self is doing the questioning? If personal identity is not a deep further fact but rather a matter of psychological continuity and connectedness, then the self who receives this death-date knowledge is not strictly identical to the self who will eventually die on that day. They are related — perhaps strongly so — but the relation is one of degree, not absolute unity.
This matters enormously for your claim. The urgency you describe assumes that the knowledge of death belongs to a single, unified agent who persists intact until that fated day. But if what matters is the chain of overlapping psychological connections — memories, intentions, beliefs — then the self confronting the death-date today may share less with the dying self than we ordinarily assume. The knowledge might generate not Nietzschean resolve but rather a curious detachment, a recognition that the person who dies is in important respects a successor-self, not identical to the one now deliberating. Far from intensifying the will to power, this might dissolve the very subject in whom that will was supposed to reside.
The genuinely interesting philosophical knot here is whether such knowledge would clarify or fragment agency. I would argue it could do the latter: by making the discontinuities of selfhood vivid — the many future selves who will and will not share my current concerns — the death-date reveals that what we ought to care about is not the preservation of this self's projects, but the quality of the psychological connections we forge forward. That is a different imperative than the Übermensch's self-overcoming, and in some ways a more demanding one.