If you are going to say that John-morality and Mary-morality are different things, that is effectively conceding that they are subjective.
The focus doesn’t have to be on John and Mary; it can be on the morality we’re referencing via John and Mary. By analogy, we could talk about John’s hometown and Mary’s hometown, without being subjectivists about the cities we are referencing.
What could ‘right’ and ‘wrong’ mean, beyond the criteria used to make the judgment?
Sure, if you’re talking about appealing to people to change their non-fundamental values to be more in line with their fundamental values. But I’ve still never heard how reason can have anything to say about fundamental values.
So far as I can tell, only by reasoning from their pre-existing values.