Assuming that the potential PoDs occurred within the 19th century in order to minimize butterflies, I still think that it would be highly unlikely.
China could probably have been able to modernize somewhat by 1900 with a PoD before 1870 or so, but its general ethnocentrism had historically prevented it from looking outward, and its size would have prevented it from enacting changes on a widespread scale. Also, the Qing was ruled by the Manchus, although most of the population was Han Chinese, which could have caused ethnic tensions during industrialization, while other minority populations, mostly located in the north and west, could have caused further difficulties if they made more direct attempts to assert independence.
On the other hand, Korea, under the Joseon dynasty, had been a tributary of the Ming and Qing for over 500 years, which limited its ability to grasp the situation outside its borders, even after the Opium Wars greatly weakened China. France sent an expedition to the peninsula in 1866 due to religious reasons, and the United States sent some warships in 1871 due to the General Sherman incident. However, due to Korean resistance, and Europe's general disinterest in the area, it was not until 1876 when Joseon was forcibly opened after Japan forced it to sign the Treaty of Ganghwa. Neither the Heungseon Daewongun, who had been ruling as regent for his son since 1863, nor the Andong Kim clan, which he had overthrown in order to restore power to the monarchy, would have been willing to accept Western intervention.
A more direct approach from the Western powers would have probably turned Korea into a colony or a protectorate, which would be out of the question in terms of the OP. The latest possibility for reform that I can think of would be the Gapsin Coup in 1884, in which a pro-Japanese faction attempted to enact structured reforms on a widespread scale, although it was suppressed a few days later when the queen decided to oust them with backing from the Qing. At the time, the monarchy's policies were focused on balancing the different factions supporting Japan, China, and Russia, so it would have been very difficult for Korea itself to concentrate on reforms with set goals in mind. By the First Sino-Japanese War in 1894 and the establishment of the Korean Empire in 1897, it would be too late for Korea to escape Japanese influence.
In addition, Joseon would need to maintain a population of around 20 million during the 19th century. For comparison, its population had tripled to 18 million within 150 years or so from 1600 to 1750, mostly due to the importation of cash crops as a result of the Columbian Exchange. However, the population actually decreased to 12-15 million by 1850 because of overcrowding due to the lack of major cities, and the capital/largest city had no more than a few hundred thousand inhabitants by 1900. In other words, reorganizing and building new infrastructure would be necessary for changes to be made on a widespread scale and have a greater impact on society, which would be extremely difficult due to Joseon's generally negative stance on foreigners at the time.
The countries in Southeast Asia would also be difficult to industrialize. Siam had occupied what is now Laos, Cambodia, and parts of Burma, Vietnam, and Malaysia by the 19th century, but due to gradual incursions from the British in the west and the French from the east, it lost almost half of its territory and was eventually surrounded and maintained as a buffer state between the two. As a result, Siam probably did its best to enact reforms and industrialize given the conditions at the time. Although having more states established in Southeast Asia by the mid-19th century could lead to a different outcome, it would still be a double-edged sword as the European powers could set them against each other by creating rivalries, as it had done with other colonies.