Thanks for the speedy reply! I'm still pretty sure I'm missing something. The two orientations I can find for the bottom left both seem to be impossible:
1) Right-facing doesn't work since it touches the top-right shape three hexes long (and that long shape can't take the other orientation since that would touch the top-left shape)
2) Left-facing doesn't work because it requires the spinner to be white (which leaves you with an extra hex)
Here's how I see it.