I found it faster to use the hose outside. Granted, I didn't use Argos, as it's not sold here, but playsand, yeah. I used the swish-in-a-bucket method in the sink downstairs, running water continuously, and then I figured I might as well try the other method, where you take the bucket outside, stick a hose in it, and turn it on. The water running out of the hose at the bottom of the bucket takes over the swishing/swirling part (cold water hurts my hands, man!), and I swear, it took less time. I just tipped the bucket over somewhat every now and then help clear out the floating sand, and before long, whatever sand was stirred up would settle almost immediately and the rest of the water would be crystal clear.
However, it's not such a fun idea in the middle of winter...