More to the "even-distribution" question, I'd recommend your idea of water distribution. I'd use spray nozzles - they're designed for relatively even distribution. To that end, I'd recommend IS nozzles (lower budget) or NC nozzles (higher budget), with a distribution manifold. These will provide an easily repeatable test method. Simply dial down to the minimum levels for consistent spray (1 psi for IS, 3.5 psi for NC). Then adjust the concentration of dust in your spray solution. Use a pressure regulator to ensure consistent pressure across the spray system, and a timer to ensure the exact amount of solution sprays across the panels. Finally, as a test to the system, weigh the dried off powder at the end of the experiment on each panel to verify how much dust was deposited on each panel.
For the powder, if you have access to a very low humidity area I'd recommend powdered milk or creamer. Talcum powder is also used readily. But that's mostly a personal opinion.