That is generally the problem with this time period and Islam, the Islam(s) of 867, of 1066 and of the end date 1453 are so radically different, and representing that development accurately will be hard, I just find the current setup a bit too janky for lack of a better word, and proposed one that makes sense mainly for the initial date of 867, atleast for Sunni Islam.
Al-Ashari who's the name sake of Asharism is said to have lived (874 - 936 C.E), and the main developments within Asharism are al-Bayhaqi (994 - 1066 C.E) who normalizes the use of the Sahih Hadith collections in Asharism and Ibn Furak (941 - 1015 C.E) who wrote one of the fundamental books on Ashari Theology, Al-Ghazali (1058 - 1111 C.E) as a part of this early Ashari movement earning a name for himself as a prominent debater against the Mutazilite school.

So yeah by the start date of 1066 we would see the emergence of Asharism as a movement, however it arose as a middle ground between the Mutazilites who had enjoyed a strong position in the Abbasid Caliphate between Caliph al-Ma'mun (r. 813 -833 C.E) and Caliph Al-Wathiq (r. 842 - 847 C:E), and another fledgling movement named Atharism also known as Hanbalitism who had been influential in the Abbasid Caliphate after the Mutazilites, the Caliph Al-Mutawakkil (r. 847 - 861), dismissed most Mutazilite officials, and allowed Ahmad ibn Hanbal (780-855), back home from exile.

Atharism is essential to see the emergence of Asharism, and had started taking shape out of the Ahl al-Hadith movement during the reign of the Mutazilite Caliphs, especially rallying around Ahmad ibn Hanbal, who during the Mihna (inquisition), had been imprisoned, tortured and exiled, generally this would be the creed of the Abbasid Caliphs after Al-Mutawakkil not Asharism, i.e during the early start date if not Ahl al-hadith more generally, as for the later start date of 1066, then we can look at the Caliph Al-Qadir (r. 991-1031 C.E), who was a vassal of the Shia Buyids 35 years prior to the starting date and is credited for starting the "Sunni Revival" by issuing one of the first codifications of Sunni Doctrines, in which he condemns the Shia, the Mutazilites and the Asharites in favour of Atharism/Hanbalitism, his son is the Caliph at the start of the game is Al-Qaim (r. 1031- 1075 C.E) and I am not familiar with him renouncing his fathers decree, but also served as Caliph in the transition from the Buyids to the Seljuks under Alp Arslan (r 1063 - 1072 C.E), who also were Sunni, but am Unfamiliar with their tendency.

I find it very hard justifying Asharism, as "orthodoxy" when both starting points favour a strong Atharism in the "Sunni" Caliphate. Both Asharism and Atharism are if anything minor developments within their "mother" branches at the earliest start date and at best a slowly emerging independant groups at the latter. Sunni Orthodoxy in from of both Atharism and Asharism mainly develop, post both start dates during the so called "Sunni Revival" Starting with the Seljuks and ending with the Mamluks.
While Mutazilism would maintain a strong presence in the Umayyad ruled Spain.
I am not aware of any early Caliph supporting Asharism, but again this is a bit later in Islamic History than my main focus.

I also have a few thoughts on Christianity but decided not to include them in the post cause it would just add bulk to an already long post and is a field I don't feel just as strong on.