Undisputed? You want all demons to maintain loyalty to you? We don't have that much time... if it's even possible. Hell will just end up like Heaven, splintered into factions.
Vampires and succubi are considered minor demons. It's a fact, not an insult. And of course it can hold the son of Lucifer. It's Lucifer's cage. Of course they are clearly in there so none of that matters.
All that matters is none of them deserve the attentions of Michael and Lucifer and Lucifer and Michael do not deserve access to them. I assure you, I am motivated.