The official site states:
There are two conditions for performing Z-Moves: a Pokémon must learn a move of the same type as a Z-Crystal, and it must be holding the corresponding Z-Crystal.
With this hidden power will be broken.
You really think they would just let an abuse case like that happen? Hidden Power will obviously be treated as a Normal-type move for the purposes of Z-Move access.
If I had to guess, the attacks are universal, meaning they are both a Physical and Special Attack at the same time. This would be another reason why they can only be used once.
How do you think this will work? How will they calculate the damage of a universal attack?