"I have a large amount of sympathy. China was an Imperial power in the great age of formal imperialism, and the Uighurs were colonised by China..."

-Not quite. The Uighurs were subject to the Dzungar and rose in rebellion aided by the Qing in the 18th c. The Dzungar were utterly destroyed in a genocidal war...which is why the Uighurs now occupy Xinjiang and why Xinjiang is also part of China.