On the other hand, I am concerned that calling reflective equilibrium 'moral knowledge' might mislead some people -- especially those who equate knowledge with mathematical demonstration or scientific proof.

The larger question is whether the relativist can have good reasons to accept a set of moral principles. We could call these good reasons a justification for the principles. I think that is our main concern.

Our moral principles are part of a larger set of ideas and views including the elements in the wide reflective equilibrium:

• factual knowledge of our circumstances
• scientific knowledge, including knowledge of the consequences of various actions
• metaphysical views such as whether values are built into the nature of things
• other philosophical views such as the nature of persons

The relativist can adjust his or her moral principles or any of the elements listed above in order to create a consistent whole. The resulting system of ideas provides support for the moral principles that are part of it. As Rawls put it when he was discussing justice: 

A conception of justice cannot be deduced from self-evident premises or conditions on principles; instead, its justification is a matter of the mutual support of many considerations, of everything fitting together into one coherent view. (Theory of Justice, section 4.)

If we take this view of it, then the relativist can develop a justification for moral principles. This approach has been called the method of "wide reflective equilibrium." Whether we call the result knowledge may not be important.