It seems to me that the world-wide British Empire could surely find something that the Chinese would like to trade for other than silver and opium. Were the Chinese really so self-sufficient that they had no desire for any British wares? Or was there something else at play?
This isn't exactly true, the overall balance of trade tilted heavily towards China until the 1820's and again tilted heavily towards China from the 1860's until the 20th century but it wasn't that before then there was literally nothing the Europeans could sell to China, it's that the overall value of European exports couldn't make up for the enormous value of Chinese exports.
One European export that had long been popular among the literati were eyeglasses, I believe dating back all the way back to the Ming. See Confusions of Pleasure by Brook for an overview of Ming cultural history. Otherwise in the late 18th century a number of European manufactures found significant numbers of willing buyers including pocketwatches, tobacco and tobacco paraphernalia, and European fabrics which were actually rather in vogue in some cities of coastal China.
I know there's at least one western historian who writes almost exclusively on fashion and other material culture in late imperial China, focused on the Yangtze delta city of Yangzhou. See the various books of Dr. Antonia Finnane. I'm relaying her research as summarized in Rowe's book China's Last Empire.