This has got to be the strangest forum topic that has yet sent traffic to my web site. There seems to be some confusion in here! Perhaps I can be of assistance?
The OP in this topic was confusing in its omission of the final gastronomic destination of the rice in question. =) Your follow-up post made it more clear:
Oh right.
Still, I don't want to simmer the rice in a seasoned cast iron wok. o.O Among other things, how would I prepare dim sum or baozi and steamed vegetables at the same time? (Yes I realize manipulating bamboo baskets full of steam is rough work-- I've done it quite a bit, and I don't use protection so I'm grabbing hot bamboo with hot steam and hot condensation all over the place with my bare hands. Still, it can be done.)
I'm trying to figure out how to cook rice using a common, traditional method; unfortunately people are disinclined to answer the question and volunteer instructions for simmering rice instead of steaming it. If I ask how to get the steak to cook just right rare on the grill, is someone going to tell me to pre-heat a cast iron pan and sear it for a minute and a half on each side and I'll have awesome, perfect steak?
EDIT: Did I already mention that I also have a purpose-made rice steamer designed specifically to do this stuff?

I sympathize with your frustration. Maybe I can help you out a little bit.
That is a Thai rice steamer, which as you pointed out is a very common and traditional cooking device for rice. The problem you're having is that your sushi rice is coming out
translucent, tough, chewy, and barely sticky at all (clicky!) and not at all the fluffy white sticky rice you're after, right? The problem isn't really in your method, it's just that you're using the wrong kind of rice. That particular kind of steamer is meant to be used for cooking
glutinous rice,
not short (sushi rice) or long (jasmine rice, etc.) grain varieties of
japonica rice. Glutinous rice is the
only kind of rice that will give you the kind of results you're looking for with this cooking method, other kinds of rice just aren't suited for this treatment and will do better simmering in a pot on the stove or an electric rice cooker.
Don't get me started on how infuriating it is that restaurants call rice cooked in a rice cooker "steamed" rice when it's really just plain old simmered rice! That's a lot of where the confusion in this thread is coming from, and it's all due to a misuse of cooking terms by restaurateurs who should know better.

Some tips that you may find useful:
-- Don't try to seal the rice in a container for rinsing, that's just adding more hassle where you don't need it. Just put the rice in a bowl that can hold twice the amount of rice you're using, fill with cold water, mix well with your hand, then pour most of the water out while using your hand to retain the rice. Repeat twice (for a total of three rinses) and your rice will be as well-rinsed as it needs to be.
-- Soak for a long time. Six to eight hours at minimum. Overnight wouldn't be a bad idea. You're after a fluffy, sticky texture in the final rice, which means you need to load it up with as much water as you can before applying the steam. The steam just heats the water already present in the rice to cook it (gelatinize the starch, that is), it does
not add much water to the rice on its own. Steam is much to energetic for that, it transfers some heat and then it leaves.
-- Use a chopstick or your finger to poke some holes through a deep rice bed (
like this) to allow steam to move through more freely. Believe me, the end result is more even cooking.
-- Steam for as long as you think you can get away with (at least for sake rice). You can start checking for doneness after 30 minutes, but I don't usually even bother until my 45 minute timer goes off. Even then, I often have to add another 15 minutes for the rice to reach the level of gelatinization I'm after. For steamed glutinous rice, most Thai cooks I know say 45 minutes is how long they steam.
I hope this helps!