Should Imperial forbearance fail, you correctly identify the organs of Holy Amarr most apt to resolve the wider rebellion, however the trappings of nobility assumed by Shakor and his cadre could justify Theology Council jurisdiction.
It is interesting to note that despite his repugnant rhetoric; Shakor has remained more interested in killing or intimidating domestic threats to his criminal enterprise than making good upon that rhetoric.
I see no reason not to let him be about it for a generation or two.