The photo on the left is the recommended setup. I've experienced the same thing, cones touching and not holding the prop snugly, with some props.

I've never heard of a 'non precision' hole. APC and Master Airscrew have a stepped hole. The center hole is usually 1/4 and the bigger hole is usually 5/16 since these are very common shaft sizes for many popular glow engines.

I do not balance props unless I install one and have a vibration.