Look, I'm all for the ROC analogue for the US, but in all honesty Puerto Rico has neither the infrastructure (ports? cities? natural resources? Taiwan was extensively built up by both the Japanese and the ROC as a strategic military asset), the economic ability, or the population (about 1.7 million in 1936 while Taiwan had a population of 5.8 million in 1940) to support a US Government in Exile. The best chance for something like a US Taiwan would probably be the Philippines (Say if the Pacific States doesn't revolt the Asiatic Fleet keeps control of the Philippines). Alternatively (If Canada didn't seize them) I could see an Alaskan Government in Exile or something in the Panama Canal. Say the US seizes Panama city and from there uses the USN to control both the Caribbean and some of the Pacific. This would give it the strategic and economic importance of Taiwan along with a population to work with.