Harry took charge in the first place because he felt it was his duty and responsibility. That and he doesn't think there's anyone else as capable as he is at protecting the wizarding world. I don't know if appealing to that sense of duty will help given the circumstances of the situation. But, he values doing the right thing. He judges people based on their ability to do just that.
Honestly, he's probably a lot less stable than Sirius was. His words to Nott about grey areas were not something just said out of anger. While I know you might say all Gryffindors see things in Black and White, from my conversations with him, I would say Harry is the epitome of that way of thinking. There is absolutely no room for even the faintest shade of grey to his way of thinking. You would have to frame your arguments in such a way that it is absolutely crystal clear that his not being Minister is Black.
That's the best I've got. Harry is not one to open up, especially if he thinks you don't agree with him. At least that is my impression from the few times I've done so.