I've never been in this situation, but would it be possible to take some kind of unofficial leadership, and build your own product, without caring about the vag

I've never been in this situation, but would it be possible to take some kind of unofficial leadership, and build your own product, without caring about the vague requirements? Just do something cool, whatever. Just take a few colleagues you trust/think might be willing to go along, brainstorm some ideas and go for it. It feels to me like creating a company, but without the hard parts: you already have the money and the smart team. Create your own startup from within.