How to fight akrasia" becomes "how to align actual preferences and believed preferences" and you're no closer to a solution.

On the contrary, you're one step closer, in that you can now begin asking what your actual preferences are, and how to get them all met.

(Note that your "believed" preferences are also preferences; they just don't necessarily have the same practical weight as whatever other preferences are interfering with them. The issue isn't real vs. believed, it's preference A vs. preference B, and resolving any perceived conflicts, by thinking through and discarding the cached thoughts built up around them.)