Shanghai-style/soup dumplings in DC?
Ah, this topic comes up every few months. You can do a search for soup dumplings on this board, but the short answer is: no.
What you can get are some xiaolongbao that get about halfway there. Good meat filling with overly thick skins (Chinatown Express) or nice thin skins that always burst and so never have any soup (A&J).
I haven't tried the new Shanghai Tea House, but that might be promising.
Otherwise, I recommend getting some frozen ones from one of the Chinese groceries or ordering the pan fried beef bun at A&J, which actually has a ton of "soup" in it. Sort of like a cross between a guo tie (potsticker) and xiaolongbao.