Mr Chatfield you missed a couple of films that might possibly been on your list and certainly before Attack The Gas Station and probably My Sassy Girl (unless you're under 21 and a fan of the genre Korea has not moved out of the Hollywood mold of-the romantic comedy). Lets see:
Oldboy and Memories of a Murder are in the category of the following 4 films. All six are as good as anything to come out of Asian Cinema or anywhere else for that matter. The Chaser and Tale Of Two Sisters are about as good as it gets.
The Chaser (Korean)
Breathless (2008) (Korean)
Failan (Korean)
Tale of Two Sisters (Korean)

And maybe not of the caliber of the above 6 but certainly above 3 Iorn (which is quixotic but is a long extention for 1 idea and more of the quality of Barking Dogs Don't Bite, eg a little fluffy)
One Night In Mangkok (Korean)
The Big Swindle (Korean)
The Presidents Last Bang (Korean)

I suggest if you haven't seen these you do and then repost because I think you will agree most of, if not all these belong. Or repost this article as The Films I Liked The Most In The 21st Century.

PS You might want to watch Downfall as well.