Finding minimum-phase/allpass of transfer function
The allpass part must have its zeros outside the unit circle, so it gets the zeros of your system, with the corresponding poles inside the unit circle. You get the correct pole locations by simply swapping the coefficients of the numerator polynomial:

$$H_a(z)=\frac{2+3.125z^{-2}}{3.125+2z^{-2}}\tag{1}$$

The minimum phase part is obtained by taking the system's poles and cancelling the poles of the allpass part:

$$H_m(z)=\frac{3.125+2z^{-2}}{1-0.9z^{-1}+0.81z^{-2}}\tag{2}$$

The transfer function of the original system is given by

$$H(z)=H_a(z)\cdot H_m(z)\tag{3}$$