"projected onto the external world" isn't really correct. Moral beliefs don't, pretheoretically, feel like specific beliefs about the external world. You can convince someone that moral beliefs are beliefs about God or happiness or paperclips or whatever, but it's not what people naturally believe.

Often pre-theoretic moral beliefs are entities unto themselves, like laws of nature sort of. People routinely think of morality as consisting of universal facts which can be debated. Thats what makes them "beliefs". As far as I know nearly everyone is a pre-theoretic moral realist. Of course, moral beliefs might not feel quite the same as say beliefs about whether or not something is dog. But they can still be beliefs.

What I want to suggest is that moral beliefs ARE your utility function (and to the extent that your brain doesn't have a utility function, they're the closest approximation of one).

Recall:

Every question of belief should flow from a question of anticipation, and that question of anticipation should be the center of the inquiry. Every guess of belief should begin by flowing to a specific guess of anticipation, and should continue to pay rent in future anticipations. If a belief turns deadbeat, evict it.

A utility function doesn't constrain future experiences. Thats the reason for the conceptual distinction between beliefs and preferences. The projection of our utility function onto our map of the external world (which turns the utility function into a set of beliefs) is illegitimate because it isn't a reliable way of forming accurate beliefs that correspond to the territory.

If you want to just use the word 'belief' to also describe moral principles that seems okay as long as you don't confuse them with beliefs proper.

In any case, it sounds like we're both anti-realists.