If a rubber ball does not provide enough traction, some balled up ducttape (sticky side on the outside) might. I’ve had some success with this method, worst case scenario you’re left with a sticky case back, which can be rubbed off with a bit of alcohol.
100% an Omega Seamaster Pro 300. Probably a mid size, no reason to assume it’s fake. My guess it’s a 212.30.36.61.01.001