Ok, I will take some shots at this.
Assuming that we do not go too far in the past, I would say there are some areas more likely than the other, obviously....
1. Korea is almost certainly a no, as far as I know, it lacked the population base and power relative to its neighbors to achieve such modernization. It would be possible if Korea was off by itself, but it is almost inevitably forced to capitulate and kowtow to one of its neighbors, likely China. 3/10
2. Oman is an impossibility, it lacks the manpower to achieve modernization without oil and massive immigration. It's growth historically and in modern times has to do with the competence of its rulers and steadfast stability seemingly inherent in their political system. This however, is not near enough, even when at their height, they were exceedingly minor, one would have to go far in the past to change river systems and ecology to change Oman's growth or some sort of tech advantage. 2/10
3. The hordes of Central Asia are a dead breed for obvious reasons. They are condemned to play the great game unwillingly whilst they attempt to preserve a backwards culture and lifestyle. This would include Khiva, Bukhara, etc... Assuming we do not go far enough back to do the rising Shaybanids, but it still is mute, it would only stand to be a more formidable opponent for Russia and butterfly the Mughals. 0/10
4. The Durrani is an interesting possibility, however it, despite being a colossus in the 1700s, is doomed essentially. They were simply a hyper Khiva, with some modernized military, their system of governance and intellectual produce was primitive and steeped in traditions of the past pushed further and further. They also were decentralized, but in a terrible way, not in the good way with merchants. Decentralized in the way of exceedingly backwards khans and imams ruling the cities and bandits ruling (often at state permission) ruling vast swathes of countryside. Progress in any way other than progress in destruction of the regime is possible. 2/10
5. I am not too familiar with Punjab/Sikh empire, I assume they could possibly, but their power is of course hampered by the powers to their west and by a lack of an effective port. 4/10
6. Yemen is also an impossibility, it was an area of extreme Ottoman interest and lacked stable rule as that of Oman. However, it has the manpower to possibly create industry without oil, especially in Sa'naa. It would need changes to maritime practices and a removal of Ottoman interest, either in complete butterfly of the Ottomans or some sort of complex Yemeni-Burji-Portugese alliance. Also Yemenhas the possibility to control Red Sea trade and expand into the areas of Harer, gaining subjects and more base to its state. However I would say it is still highly unlikely. 3/10
7. Iran's best bet is simply a long strand of effective Safavid leadership, without such a disastrous diplomacy with the Ottomans. Possibly, an Iran that focuses on trade, rather than playing geopolitical games against Ottoman and Russian powers. The Afsharid is an overrated dynasty, whether one likes it or not, the Afsharid is less likely, it was built only off the conquest of a single ruler who got lucky in India, gaining cast riches. The Safavid however, as decadent and intellectually outrageous they were, gave Iran the first serious growth and stability since the 900s.
ways to give the Safavids more of a chance would be:
- lessen the importance of religious legitimacy. The reason this is a problem is that the Safavid throne became exceedingly decadent in its reign leading to a worse and worse relationship with the Ulema and disillusionment. If there is less direct responsibility on the Shah to be so pious, the Shah's decadence can be more easily hidden and not so treasonous.
- the Qizballi should be empowered and given or have certain powers over provinces and have interest in power, more so than otl. This could create a militarist regime that understands disadvantage or the Qizballi becomes overtime, with a peaceful Safavid regime, a trade or cultural entity like the Samurai did in Japan. This could give incentive to locals to accept modernized methods of rule and decentralized trade without the problems found in Durrani and Khiva.
- a relatively peaceful Safavid regime, without atogonizing the Ottomans, the Safavids could avoid conflict with external forces. It then, if decentralized enough with the Qizballi, could focus more on internal issues, like power conflicts, in the same manner as Japan. This would limit the possibility of foolhardy imperialism into backwards lands in Central Asia, which draws Iran into conflict with the heavy hitters (Russia, Mughals, Britain and Qing). Also, once a power struggle is limited, it could be possible for Iran to isolate itself relatively. 6/10
8. In terms of Egypt, it is exceedingly unlikely, after Ottoman conquest. A continued Burji might be possible, especially if framed a certain way. The problem is that despite the cultural flourishing during the Mamluk era, they were, especially the Burji, vicious in succession crisis and lacked stability. Furthe the Burji was so long ago, it is unknown to how they would develop, as well, their performance against the Portugese was not satisfactory. Likely Egypt would need a new Mamluk dynasty, but keeping the formulas that made their previous iterations culturally and scientifically the best in the Islamic world. Over all, Egypt has the population to support a good modernization effort, but the earlier the better, afterward it becomes very unlikely. 5/10
9. I am unfamiliar with Southeast Asia...
10. I have very little knowledge of India, outside of the Mughals. Who I find unlikely to modernize in any serious way, especially economically. Really you would just see the Mughals look like the Qing dynasty if empowered.
-tolerance is not a necessity for modernizing anything.... Mughals not having Aurangzeb disappear is only one part of it. It is far more difficult to change such a heavily entrenched court royalty culture, which sees itself beyond approach. The Mughals are likely doomed either way, elegance only goes so far, as the Qing learned.
10. The Ottomans were basically modernized.... I mean, just because they were deeply decayed, doesn't mean they didn't basically modernize everything. If you say they weren't modernized, then neither was Russia.
11. I will let RousseauX address questions relating to China.