I'll need lots of sleep before I look at the whole post, but I'll try this bit for now.. First, what is 'intelligence'. We, humans, set the parameters on that term. But we can at least state that the existence that gives rise to us supports our attributes. So whatever we call 'intelligence' derives from the existence that supports us.
Now, wave behaviour doesn't explain the fringes. It models them! That's an important distinction because what science shows is that electrons, photons, are NOT waves, or particles, but can appear as either according to context. What they actually ARE is anyone's guess. All kinds of new models may be made to 'explain' them, and we may never be sure if we have reached the bottom of the rabbit-hole either. What we do already know is that links beyond those modelled in previous theory exist, quantum entanglement being a current name for such. Given that almost every atom, if not EVERY atom entirely, in our bodies has been put through a star at some point, the residuum of past entanglements and interactions is so profoundly widespread that there is no certainty of a local 'store' for intelligence or any other manfestation of pattern. The fact that one tiny photon can be assumed to pass from source to interference fringe on screen at light speed means it has NO time to pick up info about the other slit, any 'normal' way to do this means something must delay, or go out of its way! So we already know that the photon itself either does not store this patter internally, OR that its extent in existence is vastly greater (and nonlocal in the wierd-physics sense of the word) than previously thought, and that we haven't modelled them well at all yet. Nothing new there though, most people can feel that fact deeply, even if they don't know the science.
Btw, given that we define 'intelligence' on our terms, I can't use that word about a star, but I bet that if humans live long enough, stars will be found to have a much more complex nature than anything yet discovered about them. We already know they're not nearly as inert as most humans in history thought they were, even up to last month. They get more surprising the more we know. Really dumb things usually get more boring when we do that.
EDIT: I read the rest of your post where it answered me, and I think my bit just now deals with my take on 'intelligence' about as well as I can do it right now. About probability, I'll use Samuel R Delany's words, from Time Considered As A Helix Of Semi-Precious Stones. Awesome story, with the longest title I think I ever saw... He said (attributed to Edna Silem in the story) that "Probability is an expression of our ignorance, not of our wisdom".
Got to sleep now. After which this many-headed hydra of a thread will likely have mutated again beyond easy recognition. Viva thread...