  As proposed by Bambi and Modesto, rotating non-singular black holes can be
constructed via the Newman-Janis algorithm. Here we show that if one starts
with a modified Hayward black hole with a time delay in the centre, the
algorithm succeeds in producing a rotating metric, but curvature divergences
reappear. To preserve finiteness, the time delay must be introduced directly at
the level of the non-singular rotating metric. This is possible thanks to the
deformation of the inner stationarity limit surface caused by the
regularisation, and in more than one way. We outline three different
possibilities, distinguished by the angular velocity of the event horizon.
Along the way, we provide additional results on the Bambi-Modesto rotating
Hayward metric, such as the structure of the regularisation occurring at the
centre, the behaviour of the quantum gravity scale alike an electric charge in
decreasing the angular momentum of the extremal black hole configuration, or
details on the deformation of the ergosphere.
