We ate at Sushi Tenn tonight and walked by Mizu 212 and made a mental note to try it out. I've only had genghis khan (the korean version) at Seoul Garden on Olympic near Vermont--very good and you get plenty of veggies with your beef and even noodles (like udon) at the end in the broth! Yummy.
It's too bad you're limiting us to the tiny area between WLA and the San Gabriel Valley. I'm sure you'll miss a lot by such a severe limitation. But seriously, you must be jonesing something special for shabu shabu if you're opening up the area that wide.
Anyway, for a shabu shabu jones like that, you deserve Kagaya in the Honda Plaza in J-Town.
It's not cheap, but you get appetizers and dessert as part of the meal. The ingredients are top notch, and the service is very good.
Give it a try. I think you'll like it.
418 East 2nd Street (at Alameda)
(Its in a mini-mall and depending how you approach, it may not be immediately visible from the street)