I wrote a rather basic J-ish interpreter, but it was understand the mindset of the language, rather than to have a practical implementation. (I don't think I have it anymore, but it was only about two pages of Lua.) To do it well, real experience with J/K/APL would probably be necessary. It wouldn't need to be absolutely compatible with K, just a similar language.
FWIW, there's A+ (http://www.aplusdev.org/), but I would far rather stick to the ASCII character set.
Unfortunately the source is rather poorly coded - it's Arthur's "K in every language" style of C - and A+ has a lot of assumptions that I'm not comfortable with. I'd love a modernized K interpreter suitable for use by stylish gentlemen. Which perhaps could be the name..