Can the Kerr interior be consistently reduced to a 1+1-dimensional canonical model with radial and rotational sectors?

The Kerr spacetime has an axial (U(1)) symmetry generated by ∂φ. I am interested in canonical reductions of the Kerr interior motivated by loop quantum gravity and midi-superspace quantization.

A first reduction by the axial symmetry would naturally leave a (2+1)-dimensional system, with the remaining spatial coordinates r and θ. However, I am interested in whether a further, mathematically consistent reduction can lead to an effective (1+1)-dimensional canonical system.

In particular, I would like to know whether it is possible to formulate such a reduction in terms of two coupled canonical sectors:

a radial sector describing the radial geometry, and a rotational sector encoding the non-zero angular momentum of the Kerr geometry.

Schematically, the desired reduced phase space would have canonical pairs of the form

(Eˣ, Kₓ), (Eᵠ, Kᵠ)

or an equivalent set of variables, with the rotational degrees of freedom retained rather than imposing spherical symmetry.

My main question is:

Is there an established canonical or midi-superspace reduction of the Kerr interior that consistently performs this additional reduction from the axially symmetric (2+1)-dimensional system to a (1+1)-dimensional system while retaining the rotational degrees of freedom?

If such a reduction is possible, what additional symmetry assumption, gauge fixing, or truncation is required? Conversely, are there known obstructions to separating the reduced phase space into radial and rotational canonical sectors in this way?