744: Umayyad Caliphate collapses and is replaced with the Abbasid throne. Abbasids keep their early character and come to an agreement with the Byzantines similar to the Fatimid-Byzantine relations. Pilgrimage to the Middle East becomes common for Christians and the Abbasid take an ambivalent approach to the Byzantines in regards to their Anatolian provinces and vice versa. The Abbasid then succeed in murdering the entire Umayyad family and secure their strict claims to the caliphate and sets up vassal states in the region. This will limit end prematurely any Umayyad restoration attempts in Syria and bring Syria closer to Iraq.
800: Crush the Mu'tazila and their sect by incurring a strict crack down on their operations in Baghdad. This will be at the expense of Islamic learnings in the short run, but will stop the takeover of the Abbasid court and remove the possibility of the Mihna (inquisition). Stopping the Mihna will remove the impetus for the rebellions by the Khawarij as they will lack the support for their wars against the Abbasid in the Ninewah province. This also removes the major reason for the Mamluk capture of power and allows the Abbasid throne to prosecute total war upon the Saffarids and other traitors to the Abbasid throne.
810: Ali bin Muhammad al-Dibaj is killed by a Shi'i mob in Bahrian trying to claim descent from the Shumaytiyyah. His death is compounded with an Abbasid conquest of Armenia and making all the inhabitants Dhimmi. Georgia is then in turn a vassal state. The Armenians due to their conquest are no longer slaves, but dhimmi and on the frontiers. They thus experience slight population growth as opposed to a deep decline due to war. In the same timeframe, the Zabul remains unconquered as does Ghandhara. These areas then become heavily fortified to Islamic invasion or at least slowly receding as opposed to being consumed completely and wholesale. Turkish Mamluks arrive as otl, but Turkish states outside of the Islam, begin to draw nearer to China or across the Pontic steppe following the path of the Huns before them.
900: Due to the changes of the Turkish path both splitting them numerically and politically, the Ghaznavids are butterflied and their conquest and India remains relatively closed to Islamic invasion from the North. The result is India continues to grow larger than otl. Combine this with trade between Islamic states, and population really begins to boom in both Arabia and India. Over time, as well, the Somali states benefit from the trade and develop further. Maqdishu becomes even larger as it accepts suzerainity from the Abbasid and trades more with India.
930: Turkish conquerors arrive in Ukraine and Russia. The subsequent Turkish states form a powerful kingdom in the Ukraine and unite it using Christianity and makes substantial deals with Byzantium. The Turkish state then invades the Baltic and starts the wars upon these peoples earlier and with less casualties than the later wars in the 1200s. Turks arriving in the far east, form states on the west of the steppe and wage wars incessantly with other groups such as the Mongol and Manchu. This limits the power of Nomadic hordes in terms of pouring deep into China. Meanwhile, China continues to develop well, and extends trade into south Asia.
1000: Integrate the ideas from the Mayan gaining trade access into the tl.
This si a major start. Without the Zanj revolt and the massive disruption of Iraq which brought it past the point of saving, the population would be far, far larger there. Then what you need to do is avoid thirty years wars and other things. That combined with a wanked Abbasid period in terms of stability and economics, larger Hindu/Indian population, no Mongols, no fall of Byzantine power, no Saljuq Empire, etc... you end up with a much larger population of the world by 1500 to then do more work with to then take it into 1900s.