Can a “mindless matter” model give a single, coherent account of all three?
Yes.
Or does positing an organizing Mind provide the simpler and clearer explanation?
Not at all; It fails to explain anything at all.
In the "mindless matter" model, we assume the spontaneous existence of nothing other than energy and some simple physics. The subsequent development of consciousness is a long and complex process, all of which is now well understood.
In the "organizing mind" model, rather than having a set of steps that explain complexity and how it arises from simple building blocks, we have a complexity greater than the most complex thing we know - the human mind -
assumed as a starting condition.
The question "how do things like us - living, thinking, things able to reason - come to be?" cannot be answered by positing that an even more powerful thinking entity existed first.
It's like the old story of the lost motorist in rural Ireland, who stops a local and says "Can you tell me how to get to Dublin?"
The man thinks for a while, and answers
"If I were you, I wouldn't be starting from here".
To respond to the question "How come we see such diversity and complexity as exemplified by our ability to reason and problem solve?" by suggesting some entity with
even greater reasoning and problem solving powers, is not answering that question at all; It is making things even more inexplicable than they were to begin with.
We didn't know how to explain the origins of the universe we see; Now we invoke God, and are left with no explanation for the origins of God. Which helps not one tiny bit.
There are an infinite number of possible models for the beginning of the universe, and its subsequent development; But all those that do not START with something simple enough to plausibly occur spontaneously from nothing, are worse than useless.
If God knows all, then He is more difficult to explain than His creation, which his omnicognizance must encompass; And invoking Him gets us further from an answer to the question "Why are we here?" than we were to begin with.
To describe this counterproductive invocation of a deity as "the simpler and clearer explanation" is absurd and perverse; Nothing could be further from the truth.