Hmm. That looks a bit over-complicated to me. I'm not sure why you wouldn't just combine those into one tub. So long as the water has to go through the chiller first, you should get a pretty efficient heat-exchange regardless of whether or not the pump was in the same container as the chiller or not.
As to better ways, I'm sure there are some, but that depends on what you mean by 'better'. Think of it this way. In order to distill, you have to put a BUNCH of energy into heating the liquid up to vaporization, and then you have to take just as much energy back in order to condense it back down again. Be this in the heat energy necessary to convert ice to water or the electricity necessary to power an active cooling system, you still have to spend it. Even if you use nature to help you, you still need energy. Lets say, for instance, that you have a complex system of little pipes that spreads the water coming from your still into a large, thin waterfall that then plummets 20 feet, giving most of its heat energy back to the air. You would still need to spend energy pumping it up 20 feet against the force of gravity.
Now, if you, personally, want to save energy ,spent in picking up, moving and replacing the ice, for instance,, you could create some kind of active cooling system. You could, in theory, use an active vapor phase cooling system from a refridgerator or something, but you'd be
exchanging the energy necessary to make the ice for the electrical energy needed to power the cooler.
Give and take ;,