I know this thread is super old but thought I'd comment anyways.
I've found a better way to culture black worms, and probably tubifex the same way.
I got a small aquarium and put sand, then gravel in it. Just gravel should be fine, or just sand. I filled it with cycled water and ran a small air pump to it. I also dumped in a clump of java moss. With both of these things, the air pump and the java moss, you don't need to keep the water shallow. My water level is almost as high as the rim on my aquarium. I keep it at room temperature. I make sure not to over feed them and I do a water change about once a month, although maybe once a week would probably be better. The more they're fed, the more worms you end up with, but that also requires more water changes. They would probably benefit from a small sponge filter.
When I need to harvest some, I turn off the air pump for about an hour and the worms, starved for O2, climb out of the gravel trying to get to the top of the water.