I see your point of course, but one goes there more for the ambiance. I don't know of any Chinese restaurants that are in temples that date back to the Yuan Dynasty. One does get a bit tired of the local faire after a while. Of course, for duck, I would recommend if you want something quite impressive:
Gui Gong Fu, Da Fang Yuan No 11
Off Da Fang Jia Hutong, East of Chao Yang Men Nan Xiao Jie
For something more humble, there is Li Qun 利群烤鸭店.