= Solution
For axis unit <vector> $\hat\omega$,
$$
T=\frac12\sum_i m_i|\omega\times x_i|^2=\frac12I\omega^2,\qquad I=\sum_i m_i|x_i-(x_i\cdot\hat\omega)\hat\omega|^2.
$$
For a body, replace the sum by $I=\int\rho(x)r_\perp^2\,dV$.
For the hollow ball,
$$
I=\frac25M\frac{R_+^5-R_-^5}{R_+^3-R_-^3}
=\beta MR_+^2,\qquad \beta=\frac25\frac{1-\mu^5}{1-\mu^3}.
$$
Energy conservation and $v=R_+\Omega$ give
$$
v=\sqrt{\frac{2gh}{1+\beta}}.
$$
The factor $\beta$ increases with $\mu$, so if $\mu_A>\mu_B$, ball B accelerates more and arrives first. Moving the cavity off centre removes material with a larger lever arm and lowers the <moment of inertia> about the centre of mass; despite the resulting wobble, ball C therefore rolls down faster than A.
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