KenK--
I've had a PT Aurora for a couple of years now, & was initially plagued by the same problem: Since the case is translucent rather than opaque, some light is lost downward, which illuminates any dust or grime on my lenses & causes glare. (Mine is blue; red is also available, & I think I've seen an OD/camo case advertised--it might not be translucent.)
Though both will work, wearing a cap or your Tilley hat is a temporary solution, at best. I solved the problem permanently by using a small strip of black gaffer tape (more versatile than duct tape, & available in more colors, as well).
I covered the bottom portion of the Aurora, right up to the edge of the clear "lens" portion, blocking any downward-escaping light, and permitting me to use the headlight without other headgear. Trimmed to fit, it's practically invisible. The case is fully functional relative to opening to change batteries & adjusting the angle.
The only down side, if you consider it one (& I don't), is that the logo & name are covered by the tape. Pity... <img src="/images/graemlins/smirk.gif" alt="" />
David