I think we are close.

Certainly close enough to hope to agree on a set of rules, if not completely on personal values/preferences.

We have an explanation of preference in evolutionary psychology, but to my mind, a justification of its significance is necessary also.

I don't really recognize a distinction here. The explanation explains why preferences are their own justification in my view.

Clearly, we have evolved certain intuitive goals, but our consciousness requires us to take responsibility for them and modulate them through moral reasoning to accept realities beyond what our evolutionary sense of purpose is equipped for.

I think I at least partially agree - sometimes we should override our immediate moral intuitions in light of a deeper understanding of how following them would lead to worse long term consequences. This is what I mean when I talk about recognizing contradictions within our value system and consciously choosing priorities.

The desirable cognitions should be maximized in the aggregate and the undesirable ones minimized.

This looks like the utilitarian position and is where I would disagree to some extent. I don't believe it's necessary or desirable for individuals to prefer 'aggregated' utility. If forced to choose I will prefer outcomes that maximize utility for myself and my family and friends over those that maximize 'aggregate' utility. I believe that is perfectly moral and is a natural part of our value system. I am however happy to accept constraints that allow me to coexist peacefully with others who prefer different outcomes. Morality should be about how to set up a system that allows us to cooperate when we have an incentive to defect.