I got it to work, but I feel like I cheated.
First, I polished the bottom of a Mountain Dew can using my thumb and a lot of toothpaste. Took about 20-25 minutes. Shiny, formed a reflected image, but fuzzy. A little Flitz fixed that. :-)
I've never started a fire with anything other than matches, so I was guessing at tinder and technique. I used cotton gun cleaning pads smeared with a little charcoal from the grill. The charcoal made the cotton dark enough to really absorb the sunlight well.
After just a few seconds, the cotton smokes nicely. I never could get it to ignite, though. Tried different ways of packing it, holding it, fraying it. Same result.
I finally got a fire by getting the tinder smoking nicely, then wrapping it in some dry grass (easy to find in Florida right now) and blowing, gently, for a minute or so. smoke, smoke, Smoke, SMOKE, Flame! Yay!
What would make a better tinder? And if you're going to do this "for real", what could be done to the standard cotton ball / vaseline tinder to make it more appropriate for solar powered lighters like this? I'm also curious what natural tinders work with this technique. I tried the dried grass by itself, but it would only smoke a little bit, going out instantly after I took it away from the can.
(I say I cheated because of the Flitz and charcoal. But then, toothpaste isn't in my PSK either, so...)