Well, there you go; no need for the rectifier then. Now, about dimming and low voltage at idle, you'd best read up on what operating voltage the HID kit is specified for. If it can't operate under 12 Volts you can, among other things, install a DC-DC converter circuit between the HID kit and the sleds electrical system. This circuit can be able to output 12 Volts with an input voltage lower than this. So if the input voltage drops, it will draw a higher current from the sleds electric system to drive the HID kit at it's rated nominal voltage; or in laymans terms: no dimming. Of course, this only works if the sleds electrical system can output the required energy (Watts) that is required. Say, if the sled only outputs like 30 Watts at idle, there is nothing one can do, other than re-wiring the stator to outout more energy. From my memory, a High Intensity Discharge lightbulb has a rated energy draw of 35 Watts, so the sled has to output at least this much. Also, it has to supply power for the spark plugs, instrument lights and the tail lamp.
However, I must add, constructing a complete DC-DC converter circuit from scratch is something I would not recommend to anybody other than an electrical engieneer. The math is fairly complex and one must have a profound understanding of how every electrical component and term works. I'd rather just pick up a box from eBay or whereever that one just plugs in - and it works.
Another option comes to mind; turning off the headlights at idle. This can be achieved by using a Zener diode in conjunction with a relay. The Zener diode only conducts current when a specific voltage is applied to it, so when the sled is idling and outputting maybe 9 volts, the HID kit is turned off via the relay. However, when the HID kit turns off, those 35 Watts of energy is again available to be used for something else, and as this energy is made available to the sled, the voltage rises, and triggers the Zener diode and relay and then the HID kit is suddenly alive again and we are back to square one with the exeption that the light is turning on and off again maybe once a second. Complex stuff, I tell you.
- Then again, maybe the HID kit is rated for a lower voltage and will light up with maybe only 9 Volts, who knows?