If you can do it without God changing your nature then you are your own savior. By nature you are good enough and smart enough to Make the good choice to follow Christ.
So are all those verses about the “natural man” just empty words? Or is natural man indeed incapable of independently turning to Christ and your whole premise false?
Your statement doesn't make sense. Allowing Jesus to save you does not make you your own savior, it makes Jesus your Savior. Accepting a free gift does not make you the giver of the gift. If you are offered a gift you didn't earn and don't deserve and you accept it, that doesn't mean you earned it. Accepting Christs gift isn't the payment for our sins, the payment was death on the cross.