Yes but those come with strings attached. He has historically blown out budgets and taken an incredibly long time to develop games. The likelihood that either publisher will give him full creative freedom and a new studio with this setup is really unlikely.
I think people are just getting too excited and not looking at the reality of the situation. He isn't good at running a development team. He struggles to hit budgets/timelines and feature creep is very prevalent. Besides Konami sucking, there are reasons they have had strained relations for years.
If he is given a new studio by one of the publishers they will have him on a really, really tight leash. Your best hope should be that he joins and takes some sort of creative adviser role.
His only chance of actually running his own studio with minimal interference is as an independent, but getting funding would be difficult because of the reasons I laid out.
While I do agree with a lot of your criticisms of Kojima, I'd say these negative behaviors only started after he formed Kojima Productions, and was put on the board of directors at Konami. Once that happened, I feel Kojima started faltering between the pressure of having to create a game that would bring back a big enough return for Konami to offset the bombs it was experiencing with its other teams (NeverDead & several Castlevania titles all flopped during last-gen).
When Kojima was just focusing on creating a game, whether it was Boktai, ZOE, or MGS 1-3, I feel like he handily delivered both within reasonable timeframes & budgets. Him becoming the creative head of his own studio, focusing on their IP, would be a reduction of pressure that I think would benefit Kojima and his projects greatly. That, and not having to focus on creating a new engine for their game (theres no way they go into prototyping on something that isn't UE4) will ensure their development time & budget should be reasonable.