I saw this happen this morning: the minyan got to Kaddish d'Rabbanan and started, but the reader had accidentally turned a couple pages later to Kaddish Yatom, realizing the mistake only after going past where "al yisrael" should have been. A Kaddish Yatom is (I understand) valid at that place (as a substitute for d'Rabbanan), but the reader intended to say d'Rabbanan (and that's what the minyan was expecting).
I remember hearing (when learning Tractate B'rachot) that if you start to say a b'racha and accidentally say another instead, you have to go back and do it again. (I don't remember if this depended on other factors, like timing.) And according to this answer if you are in the middle of saying Shalom Rav when you should have said Sim Shalom you go back to the beginning of the b'racha, but if you only realized after you don't have to repeat. So there is precedent for going back to the beginning and starting again.
A kaddish isn't a b'racha. Specifically, it doesn't include the divine name. That might make a difference. And the two kaddishes are the same for about the first half, unlike the Shalom Rav/Sim Shalom case.
So if you realize your mistake while reciting the kaddish as in the situation I described, where you intended one and started to say another, do you go back to the beginning, or go back to the point of divergence ("al yisrael"), or just continue (changing it to Kaddish Yatom though that wasn't your intent)? Or some other possibility I missed?