To try to address your points somewhat in order:
1. Harry went to Chicago as well as "in-between" thus indicating that "in-between" is nothing special. - My points are lines of evidence, one chair leg alone can be called a stick, but together they are chair legs. It goes with the other points in that we know Harry has a soul and he went there. Alone it is meaningless, but when combined with the other points that everything we saw there had a soul (or just flat out was a soul, which might be the difference between "in between" and the spirit world Chicago). Honestly I think the stronger point of them was that while he drove around with Carmichael he saw no wraiths or other remnants of ghosts, while he often saw those things in spirit-Chicago. The only things active there were/had souls.
2. Angels everywhere - I don't consider Uriel much of an indicator since he now comes when Harry calls. Your point about the angel of death was a good one, but I will note was explicitly there to guard Forthill's soul. Honestly it strengthens the arguments about angels only being involved where there are souls - and that guard angel "in betwee" appeared to be permanently stationed there.
To strain your metaphor: I can tell the difference between a stick and a chair leg even if there is only one and no other signs of a chair. I only see one chair leg. You gotta have at least three.
So all your points are really only one point, i.e., we only see souls in Chicago Between. (You also state that we don't see any soulless entities in the limited time we spend there).
Fr. Forthill is a work-a-day hero. People like him die all the time. Angel's are likely all over the place all the time. And it might strengthen an argument that I'm not arguing with. I'm not saying angels have nothing to do with souls. I'm saying angels being around doesn't mean everything around has a soul.
3. "What comes next" may not be heaven or hell, might be applicable to ghosts - Again, not that strong an argument.
The only time we've seen someone move on to what comes next it wasn't any afterlife or divine judgment and it was applicable to ghosts. It's much stronger evidence that what comes next is Earth than the evidence you've offered for pure ghosts not being able to go to Chicago Between. Not that I'm saying that what comes next is always Earth.
We are a soul, we have a body. Ghosts can't possess people according to Stuart, that is the pervue of demons. So for Harry to go into his body, maybe for any ghost to go into any body (i.e. capriocorpus) they need to have their soul along with them.
I agree that Harry has a soul? I'm not sure what your point is here.
I like your tangent about the nature of Chicago Between. I was thinking about the substance of your next point before you made it. (Your logic was easy to follow, i.e., good). I think everybody gets a new soul in a new reality based on the overarching philosophy of freedom, choice, and consequences in the DF. Kinda like your point about will Harry have to answer for the sins of Mirror Harry? Then choice doesn't really have consequences.
Archangels definitely span the universes. It's wild to think about Denarians spanning universes. Think about how much more powerful that makes them considering experience gets you knowledge/power.
In between almost reads like purgatory, which is very Catholic. A place for souls who don't quite have what it takes to get to Heaven. But purgatory isn't for ghosts, it's for souls who haven't reached grace. This fits, in the sense that Jim uses it that way. Captain Murphy and Carmichael appear to have unresolved issues, but what would be Uriel's purpose in using a memory? It doesn't have a soul and it can't get to heaven.
Uriel does say that Chicago Between is "one of them" in response to Harry saying "That office, in Chicago Between. It was yours." It could be that Chicago Between is Purgatory and just for souls and Uriel has other offices that Sir Stuart could be being placed in, though he will be contacted by Carmichael, though Captain Murphy can transport people to places besides Chicago Between.
Yes, but Sir Stuart also said that Harry was just a ghost and we know that to be inaccurate. It is clear that Sir Stuart (and we assume Morty) is not someone educated in the vagaries of soul minutiae.
Sir Stuart definitely thinks Harry isn't a normal ghost. He does say maybe it's just because he's a wizard ghost. Sir Stuart and Morty are dealing with things they haven't seen before because of Corpsetaker when Harry arrives. Sir Stuart tells Harry that they knew something strange was going on with Harry. They worried it was something Corpsetaker did.
Also, to me, it seems that Morty is doing some pretty hard denial about Harry's situation throughout the book.
Nothing said or done by anyone in the book indicates that Sir Stuart is anything more than a ghost.
I wouldn't go that far, but I would say there's nothing that makes it more likely than not, or maybe not even "probable cause" level evidence.