Well, that was a long response. First of all, it is not unheard of that something created in one place becomes far more popular someplace else. Check out the article 7 Things From America That Are Insanely Popular Overseas, and also note that the author is Chinese. So, the relative unpopularity of any Chess ancestors in India does not rule out the the possibility that Chess has its origins there. Although there isn't much Indian literature on any possible ancestors of Chess, I do know that Chatrang became popular in Persia, and the Persians attributed the game's origins to India, not to themselves. Since India is between Persia and China, it certainly remains possible that the Persians picked up a Chinese game from Indian sources without knowing of its Chinese origins. But I am not convinced that this happened.

It seems likely that the common ancestor of Chess and Xiang Qi did not have a Cannon in it. The remaining question is whether that common ancestor is more like Xiang Qi or more like Shatranj, such as whether it was played on points or spaces, whether Knights and Elephants could be blocked, and whether there was a river and a palace. If we look at the other regional Chess variants of Asia, we find that Korea's Janggi is the only other one resembling Xiang Qi in any of these respects, and Xiang Qi remains the only regional variant that has a river. Since Janggi has Cannons, it is safe to assume that Janggi is based on a later form of the game, not on the original game. I know China and Korea have had close ties for over two millennia. I am currently watching Jumong, a Korean drama which shows relations between the Korean nation of Puyo and the Chinese Han dynasty before the time of Christ. Since you mentioned the Tang, I'll also mention that I know from The Great Queen Seondeok that the Tang were allies with the Korean kingdom of Silla, and Seondeok's nephew Chun Chu, who became King Muyeol of Silla, lived for a time with the Tang in China. Given such close relations between China and Korea, I would expect earlier forms of Chess to have made their way into Korea if indeed Chess was of Chinese origin. But, as far as I can tell, Korea only got a later version of the game. The other regional Chess variants of continental Asia -- Burmese Chess, Thai Chess, and Malay Chess -- were all played on the spaces of an 8x8 board with the same pieces as Shatranj, and they are all more like Shatranj than they are like Xiang Qi. Shogi is also played on the spaces of the board despite the popularity of Go in Japan. In general, if the original form of Chess was closer to Xiang Qi than to Shatranj, I would expect more similarity to Xiang Qi among Asia's other regional Chess variants, and I don't see that.

As a game designer, I have witnessed the evolution of my own games from inferior games. I am not always likely to invent a great game right off the bat. My best games are refinements of ideas that first came to life in inferior games. For example, Eurasian Chess is superior to the earlier Yang Qi, and Kamikaze Mortal Shogi is superior to the earlier Mortal Chessgi. Given that Chess and Xiang Qi are both superior to Shatranj, it seems likely that both are improvements upon an original game, and the evidence suggests that this game is more like Shatranj than it is like Xiang Qi.

The fact that Xiang Qi reached its current form before Chess did speaks more to the differences between China and Europe than it does to the origins of Chess. China has had a larger, more homogeneous culture than Europe has ever had for many centuries. Reasons for this are described in Jared Diamond's book Guns, Germs and Steel, which I am currently reading. With greater political stability, greater size, and greater homogeneity of culture, it would be natural for the seed of Chaturanga to grow more quickly in the soil of China than in Europe. Besides that, Europe picked up the game from the Muslims, who got it from Persia, who got it from India, whereas China and India share a common border. So, even if the game is of Indian origin, it is natural that China would have a headstart over Europe.

I cannot say for sure whether Chess is of Indian origin. But what I am fairly sure of is that the common ancestor of Chess and Xiang Qi was closer to Shatranj than it was to Xiang Qi.