If the drill bit breaks, it's a mighty cheap bit or too small. NOT SHARP...or you are too aggressive. The screws are not that hard of steel. Also, if you have decided it's OK to drill off the head, then slice a cross in it with a 1/16 thick cut off disc and chisel off the head. Reversing drill bits or easy outs are very hard to do. Very hard to get a hole in the center of a small shank screw. You will end up damaging the female threads.
Each method depends on where the screw is and what it is holding. Depends on what the end goal is. Depends on if there is a threaded hole, a nut plate, an actual nut..........that the clutch head screw is threaded into. If PB Blaster will penetrate or not for final shank extraction.
This is a pretty common problem that you will have to get good at.
Taking off the head only gets the parts apart, it does not remove the shank. But getting parts to the bench/drill press, etc. is a good goal.
