Can someone explain what's wrong with the spinning ball analogy? From my understanding, it's a pretty good first approximation of the physical interpretation of particle spin.
Basically you don't need analogy at all.
Spin is inherent property of a particle like mass, charge, etc. It's quantum like charge. If lagrangian of interaction includes particle's spin, spin effects will be noticeable in scattering and everywhere.
Analogy is only needed to not mix spin with angular momentum.
Funny how in media spin is left and right, but in science spin is always "up" or "down". :-)
This analogy has quite a lot of problems which arguably can confuse more than explain.
First thing my physics professor said in uni was "forget everything you've learned in school". This is applicable to spinning balls.