A difference I see between your recipe and other alternatives is that you don't have any other starch besides your rice. Other recipes include a good amount of tapioca or potato starch. The other difference was that other recipes used rice flour instead of rice.
You might also want to consider a change in technique. You can make rice noodles like a crepe rather than in an oiled steamer pan. Simply use a non-stick or oiled crepe pan, put in batter to crepe thickness, and let it cook until it begins to pull away from the edge of the pan. Invert and release in one motion onto a cutting board and slice.
rfusca already gave very good suggestions for the literal question from the title. However, you can also address your problem the other way round.
First, cook the soup until your noodles are al dente (but will become just right while cooling at a normal speed). Take the big pot of soup off the heat.
Second, take a small pot, and fill it with just one portion of soup per eater. Put it on the heat, and cook until the noodles are done. (Alternatively, put the single portions into porcelain bowls and microwave until the noodles are ready - it spares you washing an additional pot, but I wouldn't nuke a good soup for no reason).
Third, eat your cooked soup portions and let the big pot of soup slowly cool on its own.
Fourth, freeze the soup from the big pot. Finis.
Note that from a food safety point of view, you are better off with flash cooling the soup. But what I outlined here is probably much simple and hassle-free. Plus, 2-3 liters of soup minus a portion or two should spend less than the magical 4 hours in the danger zone while cooling. If you are doing this with a very big pot of soup and feeding lots of people, you should probably prefer a rapid cooling.
Best Answer
As a student in Singapore, we often eat instant noodles because we tend to be lazy and we lack the time to cook.
So here's how i usually do my instant noodles.
Always make sure the water is boiling hot that it bubbles rapidly. Next, you can just put your noodle in. Add the seasoning on the top of the noodles because if large amount of seasoning comes in contact with boiling water, the water bubbles out of the pot easily.
Eggs by itself, do not necessary need a hot boiling water, as long as the water is hot, it will still cook by itself.
Usually, i will place my egg about 1.5 minute later near the bubbling area (that is the hottest part of the pot) and let it boil for 20 second before offing the flames. Hence, i'll get my perfect half-cooked eggs with my favourite instant noodles.