The answer to them all is that it doesn't matter. Something is not objective when two people share the thought. Even if the entire human race agrees on what is moral, that doesn't make morality objective. So the question of "who got the label" is meaningless.
But according to label purists, such as those who must label a thing either objective or subjective, not only is the question not meaningless, but essential.
Separately,
I don't believe I ever claimed morality to be objective even if the entire human race agrees on what is moral. I never claimed it, because I don't believe it. It doesn't even make sense.
Peace