As already noted, Bollywood is already huge, and India only has a PPP GDP per capita of about $6,000. China is more insular... but honestly, so is the US. Examples:
1. When the BBC wanted to make an Independence Day tie-in on radio, Fox sold them the rights on condition that in the tie-in, the British not contribute in any way to the ultimate defeat of the aliens by the US military.
2. English-language Canal+ shows, such as XIII and Borgia: Faith and Fear, are obscure in the US, even when they're well within the range of what sells in the US today (e.g. The Borgias).
3. Europeans and other foreigners in US film tend to be butt monkeys (e.g. the European passenger in United 93 yelling "we must not interfere"), mooks (e.g. the Asian characters in multiple Scarlett Johansson movies, like Lucy, Lost in Translation, and maybe Ghost in the Shell), or nonexistent (quick, name a far-future science fiction production where the cast looks like the world and not like America).
4. The non-English-language films I watch on Lufthansa flights - presumably popular enough to be offered as in-flight entertainment - are practically unheard of in the US. Have you heard of Haz West al-Balad and Jian Bing Man? Because I can't find a single English-language review of the former, and only the barest about the latter, mainly talking about how weird and foreign it is.
Also, please scrap the "China is a relatively stable, free, and conservative society today (at least to the degree that Japan and the East Asian Tigers are)" wank. I mean, one of the reasons East Asian action films are obscure in the US is that they're often so violent they'd get NC-17 ratings, e.g. Battle Royale. (In contrast, anime is a global export.) I presume a China with the GDP per capita of Japan would be able to sell action movies better, probably better than the US - it has a larger population base, and its action movies couldn't possibly be more nationalistic than US fare (or James Bond).
The language barrier with China is something that's going to shrink as China gets richer anyway. Right now, Europe is learning English more, and this is unlikely to change, but Chinese is growing as a foreign language as China's economic influence grows. Given the number of anime geeks I know who have learned Japanese in order to relate to their favorite shows better, I think a positive feedback loop is likely, at least to some extent. If China produces a Romance of the Three Kingdoms serial on five times the budget of Game of Thrones, more people are going to learn the language.
With India, the language barrier is unlikely in any scenario in which India is rich. A richer India is a more Anglophone India, since English is the only neutral language between the various language communities in the countries, and thus the main language of business and higher education. A more Anglophone India is an India that has several times as many English speakers than the US, which means it could plausibly displace Hollywood entirely, in the same way the British film industry isn't anything to write home about. Yes, in theory Hollywood could adapt and make movies for a primarily Indian audience... but it's too American to do so, even in OTL, with slower and less surprising Indian growth than you're positing in your ATL.