OP seeks a word which captures the essence of a few extraordinary (i.e., non-mundane) experiences which, while fleeting and brief, are yet of enduring import and influence. Although words like epiphany, climax, and eureka are often applied to such emotionally-charged experiences, because the OP is dissatisfied with those words, it would seem that their synonyms would be equally unsatisfactory. I will suggest one word and two short phrases:
MOMENTOUS adjective: (a decision, event, or change) of great importance or significance, especially in its bearing on the future; of unparalleled significance
Synonyms: important, significant, historic, portentous, critical, crucial, life-and-death, decisive, pivotal, consequential, of consequence, far-reaching, impactful, earth-shattering, earth-shaking;
MOMENT OF TRUTH noun (idiomatic): a deciding instant; the time when a test determines or makes it apparent whether something will succeed.
1. the point in a bullfight when the matador faces the bull for the kill
2. a critical moment or time that tests and reveals one's true self or makes one face the truth (The moment of truth comes when you jump out of an airplane (with or without a parachute!)
A calque of Spanish el momento de la verdad, which refers to the time of the final sword thrust in a bullfight.
PEAK EXPERIENCE noun:
- a high point in the life of a self-actualizer, during which the person feels ecstatic and more alive and whole than is usual.
What is a peak experience?
Abraham Maslow, the term's inventor, says that "peak experiences are sudden feelings of intense happiness and well-being, possibly the awareness of an "ultimate truth" and the unity of all things ... the experience fills the individual with wonder and awe....he feels at one with the world, and is pleased with it ...." They are moments when you feel more at one with yourself and the world, more integrated. You feel happy, even ecstatic, interconnected and in harmony. Peak experiences are one type of mystical experiences, and perhaps one of the most interesting in that Maslow aims to talk about mystical experiences in non-supernatural terms