I added a mudguard extender, to reduce the dirt spray to the BB area. Here are the before and after shots. In both cases I had ridden on wet, paved roads, no off-road. Granted, the first one shows several rides worth of dirt, but the second one is so spotless that it's pretty clear it works.
Works rather well! This is the SKS Spoiler XXL, 53 mm wide, 150 mm long. The original Birdy mudguard is also from SKS, and the extender fits perfectly. All that was needed was to drill a hole, which was tricker than expected since the mudguard turned out to be metal-reinforced plastic. With that done the mounting was easy, and the bike stays a lot cleaner.