Why can't one hold that knowledge of evil - something itself perfectly objective - is always an inference from those other qualities? Why oppose "inferred quality" with "objective quality"?In order to answer this, I think we need to be more precise. An inferred quality is inferred using some sort of procedure. For example, the quality of a square of a number is inferred by multiplying the number with itself. However, there may be an infinite number of procedures of inference (e.g., raising X to the power Y, adding 5 to X, associating X apples with Y dollars, etc.), and no procedure is fundamentally privileged.
Now, given a specification for a procedure, I think we can show that the inferred quantity or quality is objective. Indeed, computers actually do this. However, the choice of procedure is not absolute.
If you infer from an act that the act was good, and I infer that the act was evil, we are simply using different procedures. That procedure may be rule-based or some very complex function of brain chemistry. Both procedures could be shown to give objective answers to specific questions. However, we have no "meta-procedure" to show that one procedure is fundamentally privileged over the other. We cannot say that my rule-based morality is better than your gut morality because we have no privileged meta-procedure.
For example, if I say that formal morality beats intuition, and you say the opposite, how can we show that one answer is objectively better than the other? Wouldn't that require a meta-meta-procedure of inference which is equally arbitrary?
For another example, I think one could conceivably be sufficiently precise in describing a particular Christian morality that any act can be objectively categorized as good or evil within that moral system. However, why should we choose that Christian morality in the first place? Why not Muslim morality? Clearly, we will need some meta-procedure that prefers Christian morality over Muslim morality. However, any meta-procedure that privileges Christian morality is not privileged unless we assume a meta-meta-procedure. But the meta-meta-procedure isn't privileged, and so on, ad infinitum.
In conclusion, a procedure for inference can be objectively executable, but it cannot be absolutely selectable. This is why morality, being inferred rather than intrinsic, cannot be absolute.