It seems to me that Utilitarianism can be similar to the way you describe Kant's approach: Selecting a specific part of our intuitions- "Actions that have bad consequences are bad"- ignoring the rest, and then extrapolating from that. Well, that and coming up with a utility function. Still, it seems to me that you can essentially apply it logically to situations and come up with decisions based on actual reasoning: You'll still have biases, but at least (besides editing utility functions) you won't be editing your basic morality just to follow your intuitions.

Of course, as mwengler notes, we're just replacing our arbitrary set of moral intuitions, with a cohesive, logical system based on... one of those arbitrary moral intuitions. I'm pretty sure there's no solution to that; the only justification for being moral at all is our moral intuitions. Still, if you are going to be moral, I find Utilitarianism preferable to intuitional morality... actually, I guess mainly because I'd already been a Utilitarian for awhile before realizing morality was arbitrary, so my moral intuitions have changed to be consequentialist. Oh well. :/