if you pass on the rectifier, the leds will only be on half the time. Diodes are 1 way valves for electricity, led's are diodes. Get a $5 50+ volt, 10+ amp bridge rectifier from radioshack. for a capacitor, 35-volt, 4,700uF should be enough, about $5 at radioshack. remember polarity, or the capacitor can/will explode.
I just used a pair of 4 amp diodes in series to rectify half the cycle and not have to deal with floating the ground, but yes, you will have to remove the wire from the coil that goes to the frame and hook it to the rectifier. If this coil also powers your ignition, you will run into lots of problems. Also, I don't see why you can't hook one side of the rectifier to the frame (or ground wire) and the other side to the coil output, since ground changes polarity with output. just don't wire the light's ground wires to the frame, wire them straight to the rectifier's ground. I'm planning to try this in the future.
your brake light setup sounds good, just use a 1+ watt resistor between 5 and 50 ohms, trail and error isn't hard because they're like $1 for 5.
as for the high revs, more load is your friend. Or use one of those 4 pin rectifier/regulator combos. I'm not sure how to hook them up, but I would think it would be the same as a radioshack rectifier.