(That includes the data that there are experiences, which is a difficulty for both materialism, and materialism with the magic word "soul" added.)

I dont't think this is correct. The phenomenology of subjective exprience suggests that such experiences should be "simple" in a sense - sort of like a bundle of tiny little XML tags attached to the brain. Of course, this is not to argue that our brain parts literally have tiny little XML tags attached to them, any more than other complex objects do. But it does suggest that they might be causally connected to some other, physically simpler phenomena.