Highly Experimental Design
Okay, this is my most ambitious tile design yet, so I really hope it works. But the idea has been tickling my brain for some time now.
The basic idea of this design is that balls that enter through the left or right side will be trapped in place until a ball enters through the center, releasing any balls that are trapped.
The mechanism by which this works is the flipper in the center, which has arms blocking either side passage. With a spare ball placed in the cup of the flipper (you should probably secure it in place with glue or tape), these arms will remain raised - blocking those side passages. However, if a ball enters the center passage, it will drop into the high end of the flipper, tilting the flipper down far enough to escape through the tile, which unblocks the side passages.
I haven't yet printed this to test it out, but I really think it should work. I also spent a bit of time trying to design the flipper and tile to require as little supports as possible when printing.