Excellent post found here that mirrors much of my thinking on ethical objectivity, but written much more clearly and comprehensively than anything I've ever written on the subject.
Common human prosperity and wellbeing are the goals of ethics and true, objective ethical rules are those that lead to their apex. We can analyze which ethical rules we use are closer or further away from the "true objective rules" by comparing their effects on societies on Earth, historical comparisons, logical critiques for internal consistency and the like, and reasoned discourse.
The only assumptions here are that human prosperity and wellbeing ought to be universally valued and that we have common understanding of these terms to build a consensus of action. These are not really much of leaps, especially as compared to the deontological set of rules assumed wholesale to be objectively correct by various moral Absolutists. And this way of thinking escapes the sinkhole of moral relativism where moral rules are proposed and defended by nothing more than emotion and whim.