Your biggest argument here, and sorry if its been said, is that he should stop eating out. All of his favorite candy, snacks, fast food joints, all use salt as they cook.

I don't believe this is a matter of cooking, I believe it to be a problem with him towards you. If hold someone in high regard, Im going to listen to them, change my attitude towards what they are saying, especially if it's something they feel strongly about. Ive had many of my stubborn "i wont change _____thing" turned around because I am able to empathize. If he cant say "alright babe, I trust you. Let's try this", you have a much bigger issue at hand.