I have to say, if I were and atheist (and I don't say any of this to put anyone down), I think I'd probably have to reject the notion of morals all together as empty and meaningless. Any discussion of right vs. wrong would be moot as there would be no meaningful outcome of any action. What I think I would do is simply whatever felt right, whether it was consistent with my previous actions or not. I know that's a pretty bleak picture and maybe I'd see things differently on "the other side," but from this vantage point (of believing in absolute truth) that's how it all appears to me.
Bits of that sound right to me and bits don't. Morality to me is about acting for the maximum benefit of humankind; I don't expect or look for any "meaningfulness" to it beyond that. It's about people being happy. What's the meaningfulness of that? Well, people like being happy. End of story.

So morality is "empty and meaningless" in the sense of having no results beyond its worldly results -- but it's just those results that make it important to me. What's right or wrong can be judged, though, by its effects, or likely effects, on human happiness. And yes, I do whatever feels right for human happiness; sometimes this is inconsistent with my previous actions due to the normal operation of learning from mistakes.

And I think there are different kinds of forces that impel people to act for the maximum benefit of humankind. Some, like parental love, are innate and a product of evolution -- creatures who care for their offspring are bound to outcompete those who don't. Others are not innate; often, these are society-oriented morals such as obedience to authority, which can't be expected to be innate as social change has been too rapid over the past few thousand years to have affected evolutionary change.

Maybe that's just because I reckon that "human happiness is a Good Thing" is an Absolute Truth, though, so I'm not really in the opposing camp (lacking any absolute truths) which you're describing.

Peter