Actually, only increasing flash power or ISO will alter flash exposure if the OP stops down, since flash exposure is completely independent of shutter speed. Lower shutter speeds will let in more ambient light, but judging by the linked photos, it seems the OP is going for a strictly strobe-lit face with very little ambient. If the OP is using manual flash and stops down, either the flash output or ISO needs to be increased to maintain proper exposure.
On the other hand, if the OP is using ETTL flash metering, he can change aperture, shutter speed, and ISO to his heart's content and it wont make a lick of difference; the camera will compensate by changing flash output.
