The soul is supposed to be a unity, not a collection of different modes of information.
I think you are just making up what you think the 'soul' and 'unity' ought to be, but there is no real reason to accept your idea of what it is.
Actually, no, it is not a problem for the physical model because there is a big difference between a metaphysical unity and a perceived unity.
Really? I think when one is speaking about metaphysics, pretty much anything is possible and nothing can be rules out, which makes it rather difficult to make claims that something as vague as 'unity' is completely different from something we perceive as a unity.
Some function is always lost.
The same is true for messing with your telly. There really is no necessarily discernable difference between the brain as a receiver of the soul and the brain as the producer of the mind. It is just what one choses to believe.
Not arguing for definitive proof, only for the more likely.
You can't assign probabilities to metaphysical concepts, because they cannot be clearly defined. If you disagree, tell me which is more likely: that Golliboggelotz exists or that Golliboggelotz does not exist?
It is the most metabolically active tissue in the body
That does not provide us with evidence against a receiver concept. My television set also uses a whole heck of a lot of energy.
So there is no need to suggest any entity outside the brain.
Claiming that there is no need to suggest such an entity is taking a philosophical stance. It is not a philosophical justification for taking that stance. Saying that you do not see the need to suggest Golliboggelotz exists does not convince someone who does see that need.
How does this dualism work? How does the completely other -- the immaterial -- interact with the material?
Those are good questions and I have no answer for them, but then again I am not a dualist. An actual dualist might answer it in the way most metaphysical stuff is answered: "It's a mystery".
There are more serious problems with it than there are with a physical model of consciousness.
Problems that only arise when you take a pragmatic deductive-nomological stance on philosophy, which is of course a very useful stance to take if you don't wish to worry too much about the hard problems philosophers have created for themselves. But it is a belief nonetheless.