Washing machine sound coming from top springs
One approach is to slip a shim of some softer metal (Al, Cu, or brass) under the hook. You could form a groove in the shim before placing it. Maybe the friction would be greater and the hook would not move.

Another approach is to completely immobilize the spring on the support. That would be a clamp of some kind. The simplest would be to screw a plate on so that it immobilizes the top of the hook on the spring. If the spring is moving relative to the support I think it will wear through the spring or the support or both.

Is it slipping by 'swinging' in the plane of the hook or by shifting back and forth perpendicular to the plane of the hook?