I think you’d be hard pressed to find mainstream, Mesora conscious Rabbanim that would be against it. It is already mentioned by almost anyone we look up to, such as the Arizal, Beis Yosef, Baal Shem Tov, Gra, Ramchal, the Sefer Hazohar among many others.
As I mentioned above, Rabbeinu Saadya Gaon is not famous for having learned Kabbalah, and therefore is irrelevant to something whose soul(?) origin is Kabbalah. And this, of course, is besides my earlier comment about it not really being a Stira.
Being that I expressed already — and it got a second opinion as well — that you aren’t someone else although you might have an inherited soul, we can easily have a look at Rabbeinu Saadya Gaon and see that what bothered him was the view that you aren’t a new and unique individual. That is the Nefesh. To that we all agree, it is new. And that is what the Magid of the Beis Yosef taught him.