I think it's worse to secretly wrong a friend who trusts you than a stranger. I suppose that's the sort of stance a utilitarian would want to talk me out of, but this seems a function of their societal vision rather than of moral intuition.

No, I don't think a consequentialist would want to talk you out of it. After all, the point is that loyalty is not a terminal value, not that it's not a value at all. Wronging a friend would immediately lead to much more unhappiness than wronging a stranger. And the long-term consequences of unloyal-to-friends policy would be a much lower quality of life.