YOu've got a few options, you could either try and slot what's left with a dremel tool to use a flat head to try and get it out. And if that don't work, use the dremel and some of the bits to shape the stud to where teh drill bit will want to center on it when you're starting the drill... After drilling it, use a screw extractor to get what's left out.
Most of the time when i do brake a bolt off in something aluminum, i'll just drill it large enough that i use a small pick to knock what's left of the bolt out of the hole. Then if the threads aren't in good shape use a heli-coil ( you can get them at about any hardware or automotive store ) and it will be stronger than it was new... you'd probably be looking for a heli-coil kit to give you an M6 x 1.0 thread ( that's what the honda cases are theaded factory )... I just don't know if there's enough room for a heli-coil in that area of the motor.
just have to try and at the worst case, you buy a new case half