Internal power supply??? I'm sure its accessible, not easily but accessible.
Job #1 would be to get details on the type and model of engine.
Job #2 would be to see if manufacturer has an upgrade for that type of motor.
While you do that, perhaps a stereo capasitor may be a good first step. They are meant to charge and discharge quickly based on stereo power draw for the "bass", however in your case it may be a good option to keep your headlights on.
Try this site to find a suitable match
Car Audio Stereo at HiFiSoundconnection