So I'm left asking myself whether she needs to either accept me as I am, or break up with me, or if there's some way I can change my thinking so I am intrinsically more concerned with hygiene. Frankly, I'm not hopeful for the future of our relationship.
It may be salvageable from your point of view however it takes two people to make a relationship work. If both people are not 100% into their half - then its not going to work.