I am quite intrigued by this discussion topic. Unfortunately I don't know enough to offer many helpful answers, so instead I'll ask some more specific questions that might give some guidance.
From what I've heard, the Islamic Golden Age from the 600s to the 1200s was a time of great scientific progress in the Middle East and North Africa. What kind of PODs could sustain or accelerate this development? My thoughts (mere speculation) would be that three main hindrances to the Islamic Golden Age were:
1. Christian Europe's vilification of Islam and its Crusades and other "holy wars" against Muslims,
2. Attempts by central Asian steppe nations to dominate the Middle East throughout this period, and
3. The arid ecosystems of the Middle East make for sparse populations and limit the spread of new technologies, as well as decreasing their usefulness.
If I am correct in assuming that these three factors were among many of the difficulties the Muslims faced in their scientific revolution, then the first two could perhaps be limited either by creating "distractions" in Europe and central Asia to curtail their aggression toward the Middle East, or by (somehow?) making them more cordial toward Muslims, and vice versa.
The problem of the Middle Eastern climate (#3) is more difficult to avoid without calling the Alien Space Bats, but perhaps it can be worked around by securing territory for the Caliphate(s) in more fertile areas like Ethiopia, Spain, and Anatolia, where populations can grow to denser levels more easily.
What do you think? How, if at all, could the Islamic Golden Age have been more successful? Or, alternatively, what region of the world could have produced an early scientific revolution even more successfully than the Arab world?
Please call me out on any mistakes I made in my analysis of this topic so that I can learn from them. Thanks!