We had a scientist come to our guild meetings and he was saying that bees, like humans, like electrolytes in the water. This is why they like pool water. One way to get them to come to a certain source though is to add lemongrass oil so it. Just a few drops to a gallon. It will keep them from going to a neighbors pool and go to a feeder. At least that's what the scientist said. I haven't tried it or checked with the neighbor with the pool.
But back to the OP questions, I would move the water. Not only would it be a hassle to move each time, if other bees find it the guard bees will go after them to keep them away from their hive. The stream should be ok, but you can put the cans on the porch or something also. Like said before, they like drinking off the surface of rocks so you might want to put some rocks in the bottom so they can stand on them and drink. Bees can drown in 1" of water so it will help Since that is all your using it for.
Also, don't worry. I know you spent a bunch of money, but even if you lost all your bees they are the cheap part to replace. I can get 2-3 swarms a day right now for free.
Disclaimer: I know enough to know I don't know anything yet.