As I understand it, the energy gain from a slingshot is derived from the translational energy of the more massive object, and not from the spin. The slowing down of celestial object's spin is due to tidal effects, not possible with a Born rigid material. The spin of neutron stars has been shown to decrease but as yet there is no similar demonstration for black holes.
None of this is conclusive but it keeps me hoping for real confirmation.
Dave Proffitt