I am just now building something similar in function, although I'm not interested in measuring dark sky. However, I have a few suggestions for you:
First, think in terms of the area of the sky the sensor is seeing. The shorter the focal length of the lens, the wider the area that impinges upon the sensor. Of course, the sensor is tiny, so that may not be much of a consideration. But it's something to keep in mind.
Second, use an "optical amplifier" to strengthen the signal: a lens. Surplus shops have tons of huge, short-focus lenses that were used in the now-obsolete projection monitors, and you can get a 3" objective for under $10. I found a plastic jar that fit it perfectly, cut the jar up and stuck it on, then mounted the sensor inside it. This thing was extremely sensitive: I was using the TSL235R sensor, which is not as sensitive as the one you describe, I was still getting something like 3 Hz output pointed at a midnight sky. When I realized that I didn't need that much sensitivity, I tore it apart.