I think SJs are more what people think of as Js, and actually TJs, too. INFJ is least J...J, I think. Because the J-ness would be so Fe based and lack Si, that the structure they require would be more abstract or institutional or social rather than tangible physical order, necessarily.
Fi and Ti types also have a stubborn rigidity that some people associate with "J." I have no idea why, though. If J to most people means Type A or external order and planning/schedules, I'm not sure why having rigid intellectual or moral systems internally would seem "J." Just because you're a P doesn't mean you're a blob who utterly lacks a sense of self.