Under Psychohistory, it shouldn’t matter who the leader is; what matters is the forces on the population as a whole and that populations respond to those forces in predictable ways. Individual leaders come and go and really don’t matter very much on the big-scale stuff that Psycho-History is making predictions about.

It’s the whole basis of the first several books that this “large forces acting across whole populations” model is the ‘true’ way that civilisation-scale history works and why the future history is so predictable (before stuff starts going a bit off the rails later on in ways that I’m not going to spoil).

To me, if you’re not using that concept as the bedrock of the story you’re telling, then you’re not telling a Foundation story. (It might be a quite good science fiction story of course, just not Foundation)

However, Seldon, to Raych, tells him that his decision with respect to Gaal will determine the fate of the galaxy. That's way too much weight for Seldon to place on one person in the context of the series, especially at this point unless he already knows about people like The Mule (which would be unfortunate, that'd be something best explored as it throws a wrench in your plans, not from the beginning of the series).