Chinese noodle dough breaking when pulled

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.

Kansui is a mixture of sodium carbonate and potassium carbonate, both alkaline. Since lye is also alkaline, it could serve a similar function in the dough but it would depend on the relative strengths of their alkalinity.

Specifically, alkaline water interfere with enzymes in the flour and thus inhibit the development of gluten, allowing for the dough to be stretched more readily. That being said, you need some gluten development or else the dough won't form.

Alkaline water also will change the color yellow and make the noodles slippery on your tongue. This reaction is the same one that would take when you combine soap with water.

Harold McGee wrote an article in The New York Times about the effects of alkalines.

All this being said, I've only made ramen style noodles, not the hand pulled ones. Your best bet would be to try both and see whether there truly is a difference or not... but I imagine the most traditional method would be to use kansui or jian.