I am not sure why such a space would be needed, as what you describe is exactly the role of the HM. Maybe improving the communication with the mentors could be useful or even introducing a back-up mentor. But I am not convinced on the necessity of a dedicated space. Note that mentors are, in my impression, always available so that I am not sure to see a need for this. But maybe could you share some counterexample?
Concerning the levelling thing, we have something in mind along these lines, but this is not for today ;)