I agree that hyperactive neurons currently seem to be the cause of cramping, but one slight correction. Depletion of ATP in a muscle cell would lead to rigor (basically where your muscles lock in place) and cause damage to the fibers due to the myosin heads being permanently attached onto the thin filament, f-actin (this is what happens when people die and their muscles are depleted of ATP, and is called rigor mortis). ATP is used primarily to detach the proteins that pull on each other in the sarcomeres (the smallest unit of a muscle) during the cross-bridge cycle (the process in the muscles that causes them to bunch up and contract).

Calcium flowing into the sarcomere is used to allow the attachment of the two proteins that pull on each other during contraction. SERCA is a pump that moves calcium out of the sarcomeres back into its holding place in the sarcoplasmic reticulum (this allows for muscle relaxation) and it uses an insignificant amount of ATP compared to the cross bridge cycle. Muscles will simply stop working when they reach exhaustion (no more cross bridge cycling) if there is a relatively low amount of ATP (but not depleted) present. This is due to chemistry rules like L'chatelier's principle which has to do with how much products vs reactants must be present during a reaction, or if the calcium concentration is too high in the t-tubules (little tubes that carry action potentials deep into the muscles) preventing any more signals from traveling into the cells.

So, the pain from cramps is not due to any depletion in the muscles themselves because they just will stop working (like how you feel week after doing a set of weights). Neurotoxins like sarin cause pain and uncontrolled contractions (somewhat like cramps, but to a much more serious degree) by forcing the muscles to contract to a tension much stronger than your body can handle, causing tears.

Source: major in biochemistry and many courses in human physiology