They never said there's more than one mind in God.
To my knowledge, classical Trinitarian thought does not claim that there are three minds. The Catholic Encyclopedia, which represents traditional Catholic view in the early 20th Cent, says there's one mind. "Granted that in the infinite mind, in which the categories are transcended, there are three relations which are subsistent realities, distinguished one from another in virtue of their relative opposition then it will follow that the same mind will have a three-fold consciousness, knowing itself in three ways in accordance with its three modes of existence." (article on the Trinity, Catholic Encyclopedia, newadvent.org)
The things that we normally think of as constituting a person actually go with the nature, not the Person. The only thing that isn't one is the relations. That's one reason we've all agreed that "Person" in Trinitarian theology is not the same as the common-language use of "person."
I don't think I trust your evaluation of whether a theology is modalist.
I'm with Erose on this one. I agree that persons in the common-language sense are beings, but God is one being. (Except of course when we get to the Incarnation, when the Logos is one being, but that's a different problem.)