In full suspension hanging there would be no way to avoid compressing the carotid arteries, since you are using your full weight, it is a certain death. The goal is not to break the arteries but to block them. Stopping blood flow and oxygenation of the brain:
Consciousness is often lost within 10 seconds or less, although body movements can continue for up to three minutes. It is reasonable to assume that the conscious phase is painful due to the constriction and pressure on the neck and the panic caused by being unable to breathe.
A secondary "convulsive" phase may occur, while unconscious, which can persist for as long as three or four minutes where there are visible movements of the body and limbs and drawing up of the legs. Agonal respiration sounds may be heard, the person gagging and gasping for air. Decerebrate posturing typically follows the convulsive phase, where the limbs extend and contort. A decorticate phase may follow with further apparent contortions. Decorticate posturing is a sign of damage to the brain stem and spinal cord. These two phases can last about three minutes before the person goes limp, but isolated, spasmodic body movements can continue for some minutes longer. All of these movements may be mistakenly perceived/reported as conscious suffering and struggling.
You can definitely die from strangulation, as happens in many accidents (usually children) or homicides. Although it would be the tourniquet method (or night-night as it's called on the forum). Since you're not hanging using your weight, but rather with a ligature or other material tied compressing your neck.
In partial hanging your survival instinct will save you, if you do not lose consciousness (blocking the carotid arteries) your body will make you react so that you get up (since you will be in contact with the ground) Also, you would have the discomfort of feeling like your head is about to explode (due to compression of only the jugular veins)