Ethanol would probably be classified as a natural solvent. The edge cases fall off very quickly, this can definitely be done on case by case basis without introducing onerous bureaucracy.

Even if it were distilled from petroleum?

Ethanol is not distilled from petroleum. Industrially it is produced by distilling plant sugars and starches.

It can be distilled from petroleum, and there is the key distinction that wasn't answered - are "natural" ingredients ones that could be made by "natural" (I'm assuming that "biochemical" is meant here) processes, or are they ones that are made by "natural" processes? Or is it just petroleum that is the problem?

Where does salt fall here?

Why isn't petroleum natural, when it is plant-based?

A good starting point would be to broadly classify petroleum and its products as artificial.

Apologies for so many questions, this is a very interesting line of reasoning.

What makes petroleum artificial compared to any other substance found on (or in) earth?

It seems you are proposing that "any food that has had a petroleum product added to it at any stage is artificial", which is an oddly narrow focus.

For that matter, does this definition of "artificial" extend to the range of substances that can be synthesized with bio-feedstock?

To expand on our discussion, would this mean that ethanol made other feedstock is natural, but made from petroleum is artificial?