If there is a socket bracket in place I'm afraid there is no way of twisting the heatsink. What you could do however is to try and heat up the proc, shutdown and try remove the heatsink asap. It may or may not help taking off the heatsink.

p/s on a stock hsf, I've always pulled off the proc together with the heatsink. I'm very confident that it will do any damage, btw just make sure you gradually apply the force and never ever try snapping out the heatsink.

Yup, all. Processors without the IHS(heatspreader) is a different case altogether as the contact surface between the heatsink and the core is minimal.