I've experimented with swapping around the astrological correspondences for the Major Arcana to suit my own astrological sensibilities. Supposedly the High Priestess is a purer and more noble expression of "Moon energy" while the Moon card is more insidious and takes on the interior, secretive nature of Pisces. But as the second most important "planetary" body in astrology, the Moon should really be assigned the Moon in the same way the Sun applies to the Sun; the intuitive, psychic nature of Pisces seems like a better fit for the High Priestess. The secretiveness would still be there, but it would be more sublimated, not so untrustworthy.
This also seems to make better sense from a qabalistic perspective since the modern ruler of Pisces, Neptune, is a "trans-Saturnian" planet that seems better situated "crossing the abyss," and I also like the idea of associating Neptune with Da'ath on the Middle Pillar, so there is a convergence of ideas there.
Barleywine, your knowledge never ceases to amaze me!
Being Pisces myself, I find the Moon more fitting my personality, though and I found the High Priestess often hiding just as much as you assume the Moon would.
About the personality traits of fish-people: as a card of illusions I think the Moon fits very well my habits of secret dreams and plans that may never come true, my melancholic shifts of mood, my pretending to be someone I don't feel I am. I often feel alienated from the rest of the world, misunderstood by all but my brother (who, as equal twin, is Pisces as well). But from all this darkness springs sensitivity, creativeness and spirituality at the best of times.
Judging just from myself, maybe we Pisces can be like the High Priestess, serene, solemn and mysterious, but only if we accept the wilder side of the Moon in us, that is much more prevalent in our daily lives.
There is another reason why the Moon does not unsettle me. If it wasn't for the Moon, this card would simply be called The Night or something like that. The Moons light may just be a reflection but it illuminates what is hidden rather than clouding it. That may feel uneasy at the beginning, but it enables us to travel unharmed through the night of our souls.
As I said, in practical issues, I found the High Priestess hiding much more than the Moon. When the Moon is around, there's at least the possibility to uncover the truth... with the High Priestess? No chance!