finished my targeted reread/rewatch and i can confirm that matoba stops asking natsume to join his clan immediately upon learning that natori has a paper doll tracking natsume. like, immediately. within a couple panels (manga)/seconds (anime). and then never brings it up again. here's the progression:
matoba intro/conjurer arc: matoba runs into a strange kid in a shrine and tries to choke him to death thinking he's a youkai. doesn't work. the next day, that same kid and matoba's once and future homoerotic situationship follow matoba to some random village because they're so obsessed with him. the kid turns out to be crazy powerful. after saving them from the clutches of a bloodthirsty youkai (who he may or may not have had a hand in awakening, but that is neither here nor there), he tells the kid, essentially, i'll be watching your career with interest. no job offer.
eastern forest: the kid breaks into one of matoba's houses. clearly, the universe is sending matoba some kind of message. the kid is a bit misguided, priorities-wise, but that's correctable. matoba asks him to join the clan. he says no and escapes with his insanely powerful entourage of youkai. who is this guy.
letter from the exorcist: this is where it gets good. matoba is now fully thinking, "i need to recruit this kid," right? so he sends the kid a letter with a request/demand for help on a specific job. the kid claims to have lost the letter. yeah, sure. he coerces the kid into helping him via some good old-fashioned blackmail. then during the course of the assignment, he asks him to join the clan not once but twice (in the manga) or THREE TIMES (in the anime) and is rebuffed. and at the end, during one of his recruitment spiels, what should he find in the kid's hair but a natori paper doll watching over him? so now he's thinking, "oh shit, shuuichi-san is serious about this kid as an asset." i was originally thinking that he would assume that natori is actually fully intercepting natsume's mail and stole the letter, which would be hardcore tactics that matoba would definitely respect, but when matoba brings up the letter with natsume, he says that he lost it, not "what letter?" so matoba probably thinks that natsume took the letter to natori and natori sent him there as, what, a spy? with protection in the form of paper dolls? which is hella flattering. aw, shuuichi-san, you shouldn't have! i would let you install a nanny cam in my house any time 🥰
every encounter matoba and natsume have after this, it's either entirely coincidental (abandoned station, hakozaki 2/one-eyed youkai, miharu loquats arc, taki cafe, auction arc; note that with the exception of the cafe, none of these are places it makes any sense for natsume to turn up at) or natori actually asks him to be there (homura cats arc). matoba is not making any efforts to seek natsume out. he's treating natsume as, if anything, an external consultant: he's moved from talk of natsume leaving his foster family and joining the matoba clan to the much more informal and transient favor-based economy.
so. turns out it's not much of a custody battle at all, because as soon as matoba becomes aware that natori wants custody, he backs off completely. which makes sense if you think about it. he's never actually been interested in competing with natori. with as much as he nags natori about his weakling shiki, do we really think he's gonna try to poach the first heavy natori's ever shown an interest in? get outta here. he wants natori to get stronger. he wants natori to have allies. he's probably like, fucking finally. maybe now i can ease up on the protective detail. get nanase to stop sending me knowing smirks when that line item comes up during budget meetings. you know?
but then it turns out natsume needs a protective detail even more than natori. and matoba ends up being the protective detail. that's fine. he's not looking for custody, but he is on standby to swoop in and save the day whenever called upon to do so. that's just what you're signing up for when your once and future homoerotic situationship takes a powerful but troubled teen under his wing. all part of the dance, baby.
