The "unconscious mind" isn't a real entity; it's not a "mind", in the anthropomorphic sense. It's just whatever you're not paying attention to right now, that keeps on going. If you pay attention to your breathing or your heart rate you can learn to control them. If you pay attention to your feet you'll know where they are right now. And if you pay attention to what you actually get from your "akrasic" behavior, you'll realize it's something you genuinely want.

Patri Friedman once wrote something about "wanting" versus "wanting to want". I agree that everything you do, you genuinely want to do, in the sense that you're not doing it under duress. But not everything you do is something you want to want to do.

Likewise, if I imagine myself suddenly getting infinite willpower, there are certain things I would do more and other things I would do less.

I'm using the word "conscious" to refer to things I want to want and things I would do more with infinite willpower. I'm using the word "unconscious" to refer to things I don't want to want and things I would do less with infinite willpower. I don't think it's too controversial that those are two different categories.