In case it helps, I don't actually think it does sound terribly old-fashioned, just a little folksy. The phrase is distinctive enough to notice, but 'what person under eighty' is surely an exaggeration.
And just to be clear, 'on God's green earth' is just an expansion of the basic phrase.
no way > no way on earth > no way on God's earth > no way on God's green earth
nothing > nothing on earth > nothing on God's earth > nothing on God's green earth
where > where on earth > where on God's earth > where on God's green earth
It's basically meaningless; or rather, it means roughly the same thing as
no way > absolutely no way
where > where in the world
never > never in a million years
In English you could also say 'where in God's name' or 'where in the name of the Almighty,' and maybe also 'no way in God's name.'
So yes, maybe #8 could work if we could make it negative. Could you say, for example, something like
Es kann, in Namen des Allmächtigen, doch gar nicht sein, dass wenigstens einer der beiden nicht wusste, was unterm eigenen Dach passiert ist.
Just out of curiosity, I wonder if there's a grammatical term for that kind of intensifying phrase.