With an isolated LED supply, it would be very easy to use the unused contact of the relay with the common to toggle between red and green, just need a couple of resistors to accomplish the trick. I am spoiled by having a ton of salvaged DPDT relays, but they're not really necessary.
One additional point. If you're putting a fairly large capacitor behind the bridge, I'd also suggest a small resistor to limit the inrush current to minimize arcing of the wheels as the capacitor initially charges. Even a few ohms makes a large difference.
