...but that's not really meaningful unless we assert that the gravitational energy is 0 J an infinite distance away from all mass, which sounds reasonable, but can't be proven via experiment
Well it's neither reasonable nor provable because the concept of infinite distance is itself flawed.

Surely every region of spacetime is curved? Surely your original comment was techincally correct? I mean the top of the hill, it's not "flat" except from the frame of reference of those on earth looking at it. And even then, down to the molecular level, it's not flat at all.