The voltage regulator only maintains the system voltage at 12v. It's not a current regulator.
Think of it like a garden hose. Let's say that the garden hose has a pressure regulator ( opens/closes to maintain output pressure). If you hook up a fire truck to your garden hose, there will be a huge demand on your garden hose to supply the fire truck. The pressure regulator will work over time to maintain the pressure coming out of the garden hose (that's the voltage) but the huge demand means that it's got to open up more to allow more water through (current). It's not going to be able to keep up with the demand.
If the current draw is too much, the stator coils can burn out. Kind of like putting a fork in a socket. It draws too much current (short circuit) and trips a breaker. If there wasn't a breaker there, the wiring would overheat and catch fire.
Anyway, I'd try to find out the rating of that whizzer changing system, then fuse the output. If it blows the fuse, find a lower rating bulb.
I will be visiting HF soon for one of those lights.