So, this is going to be a two part idea. First, I'll talk about Tanjiro entering the world of Bleach, and then Ichigo will make his way to Demon Slayer's world. I know I've already done both of these settings before, but I feel as though they would mesh well. I'm more focused on writing Tanjiro's journey, but that doesn't mean I won't put forth a similar effort for Ichigo.
The main order of business is to discuss how Tanjiro gets to Soul Society. Yes, I want him to become a Shinigami, as becoming a Hollow or Quincy doesn't suit the character. That doesn't mean I can't see either of those things being a possibility, I just think it'd be easier to use the Shinigami powerset. I also don't want to exclude the possibility of becoming a Visored/Vizard. Anyways, onto how Tanjiro dies and is reborn in Soul Society. The easiest method is to say he dies fighting Muzan and on his way to the afterlife, is scouted by a God/Divine Being to bring balance to another world. The unfortunate part is that his memories are erased, as to prevent knowledge of other worlds from leaking.
Now, there are two options: Either he is placed as a Soul somewhere in Rukongai or is reborn as a part of a Noble Family. Some might prefer if he were to have no familial connections, but I think it would be good to give him another younger sister as a replacement for his dynamic with Nezuko. There are two possibilities for Noble birth: The Shiba Clan and The Kuchiki Clan. Why these two? Well, the Shiba Clan would give Tanjiro some relation to Ichigo, plus members of this clan have seem to have high amounts of Reiryoku. And of course, the Kuchiki Clan has Rukia as a little sister for him.
So which of the 13 teams does Tanjiro belong in? Well, we can right away cross off the 2nd Division, they're more stealth oriented and Tanjiro is a warrior, not a ninja. We can also exclude the 4th Division as they are the medical team and Tanjiro is more likely to receive wounds than heal them. And the 12th Division is out, as it is the R&D Department of the Gotei 13. Out of the ones that are left, I think Tanjiro's personality meshes with the 13th Division. But, I feel as though he should get personal training from Yamamoto.
Let's discuss his Shikai and Bankai. I believe that he should have a dual-attributed Zanpakuto as a reference to his two different Breath Styles. His Shikai should use water in various ways to enhance his combat ability. I don't know what its name should be, but its release command should be Breathe. For the Bankai, he should switch to fire, which would match the Captain Commander's, with a name reminiscent of the Dance of The Fire God Style (Hinokami Kagura).
Now, for the reversed scenario, Shinigami in Demon Slayer.
I'm going to at least attempt to make this well fleshed out, I really want to put more effort into these dual idea chapters. It is tough to feel satisfied with the second idea when I focus so much on the main one. So, what happens if Ichigo suddenly found himself in the world of Demon Slayer?
I'm not suggesting that he died or anything. No, I'm suggesting that Ichigo goes to sleep one night and when he wakes up, he finds himself in the middle of a mountain forest. Now, my problem is whether or not to include Zangetsu with him. I'm thinking that it should depend on how his powers manifest, and I have two options for that.
First is his powers manifest perfectly, allowing the use of his Shinigami powers in his human body. He would wake up in his Shihakusho with Zangetsu in a sealed state. The second option is to tie it to the world's power using Breath. He would have a unique Breath Style, known as Breath of the Soul, or Reaper, depending on your preference.
If the second option is the one you use, then let's talk about how this affects Ichigo. He would have to learn how to push his human body to its peak. He would also only be able to rely on himself to grow stronger, as Zangetsu wouldn't be able to give him advice or help. Any Shinigami technique would be near impossible to use, meaning Shunpo would be difficult. Quincy techniques would be perfectly acceptable, bolstering his defence with Blut Vene, and Blut Arterie for offense. Hirenkyaku could also replace Shunpo, but like everything else, Ichigo has to learn and master them on his own. Maybe when he receives a Nichirin Blade, he'll begin to hear Zangetsu's voice again.
The first option gives Ichigo access to all of his various powers be they Quincy, Shinigami, or Hollow. In this scenario, he would have time to learn and master all of the various skills that his bloodlines gives him. Zangetsu would be there, helping him along the way.