Cooking Dry noodles without them being soggy

It's not too much water that makes them soggy, it's cooking them for too long in the water. Thin noodles are virtually done as soon as they break out of their dry, tablet shape. As soon as this happens, take a noodle out and test it. Remember that cooking will continue even after you drain the noodles.

You should drain the noodles well in a colander. If you are planning on stir frying the noodles, you need to first wash the starch off them - run the cold water tap over them and circulate it through the noodles with your hand (carefully, they might still be hot in the middle). They then need to be dried as much possible - spread them out on a board, pat with paper towel, and leave for ten minutes or so before stir frying (preferably in an empty wok - cook the rest of the stir fry first, then empty it, cook the noodles, and re-add the meat etc.)

Nebuk, I, too, had labored over baozi many a time, only to have them fall flat. After much searching, I came to Andrew Nguyen (who has since answered many more of my questions regarding Asian cuisines) for the answer. Check out this article by her from the LA Times.

She addresses your problem specifically:

The problem arises when the dough is stuffed to make filled buns. Whether the filling is raw or cooked, it introduces moisture into the bun during steaming and can cause the dough to cave in or wrinkle after cooking. Imagine my devastation on the occasions when that happened after hours of working and waiting.

She offers advice on how to prevent this:

At the end of the day, the best and easiest bao dough is simply made by stirring together these readily available ingredients: moderate gluten all-purpose flour from the supermarket, instant (fast-acting) yeast, baking powder, canola oil, sugar and water. I often knead by hand, but when I feel lazy, I let the food processor do the work. Regardless of method, the result is fabulous...The key is having a little fat and combining yeast with baking powder in a balanced proportion. As biochemist and acclaimed author Shirley Corriher explains in "Cookwise," working in a small amount of fat tenderizes and enables bread dough to hold gas bubbles well. That lightens the dough, she says, as does employing a two-pronged approach to leavening.

The two-pronged approach to leavening here being the use of both yeast and baking powder.