“How do you remove the poisoning agents from the denatured alky?”
Fractional distillation, starting with the right formulation of denatured alcohol. Just like making moonshine, but with a little more control.
Fractional distillation relies on different liquids in the alcohol having different boiling points. The people who apply the denaturants selected them very carefully to keep the boiling points as close as possible. It is much more difficult than you imply.