Can't prove the supernatural God

[SteveII]

Supernatural - anything outside the physical universe and its laws.
Unnatural - within our universe and laws, anything artificially created that would not exist on its own.

That brings up an interested question. Could you have an unnatural supernatural object? Say if an angel made a cake using supernatural chemical sweetener for an all-angel potluck. Huh, have to think about that. 

You can call anything you want a fairy story or made up, but you aren't engaging the question of whether the supernatural exists with anything resembling a cogent argument.

Might something like "exonatural" or "ectonatural" be more fitting?

I think supernatural covers it. Super- a prefix meaning “above, beyond.” If you use a word people are not familiar with, you will lose them from the start or just create a tangent that could waste time and effort.