I tried adding a simple reflector to the solar still and got some success. In this case, the reflector is aluminum foil taped over three sides of a box. I started the experiment running at 11:00 and ended at sundown. Every hour I re-aligned the reflector with the sun (something you don't have to do with the basic, reflector-less still.) Here's a shot of the system in operation next to the reflectorless system for comparison.
The reflector showed a dramatic improvement. The version without a reflector produced two teaspoons of water. The version with reflector produced 4-1/2 teaspoons, so about twice the production rate. Weather conditions were clear and sunny.
I need to re-run the test to be sure, but it looks like the reflector gives a dramatic improvement in the still's output. It's not enough to make the still useful, but with a few other 2x improvements we might get there.