In what situations do the answers to the inverse differ from the original? It seems to me it's just a rewording of the original question with a double negative.
("How do I not not fly to Spain?")
("How do I not not fly to Spain?")
How do I not lose money? - Don’t gamble.
How do I not not make money? - Take more risks.
A true inversion with a negative works better than the not-not structure, and it is easier to wrap your head around.