The problem with the theory of coming from Chinese Buddhist monastery is that, Chinese Buddhist monks are vegans. They are now allowed to eat meat. Keeping livestocks are also known as imprisoning the creatures. Therefore, Buddhist monastery usually don't have livestocks.
Chinese people like eating chickens know as "走地鸡” “zou di ji". Meaning, chickens that runs about. Chinese people believe that chickens that free range absorbs all the qi from the earth, giving the meat special benefits and the meat tastes more juicy. Therefore, they believe that raising chickens until they are near wild makes tastier chickens.
Chickens in China like such as the Cochin, and silkies are also raised like this. Their legs are also featherless. Therefore, what were the original stocks like? We really do not know.
China as you know has been through decades of war and destruction. The Cultural Revolution was when most were lost. For example the pekins are non-existent in modern China; because they were ornamental birds and a reminder of what "old China" use to be they were wiped out in the 60's. Not just chickens. Dogs like Shar pei does not exist in China today. Shih tzu, pekingese, chow chow also faced the same problem during the cultural revolution. They like the Langshans, only survived because some were hidden in rural areas that not a lot of people goes to.