Motivated by experiments monitoring motion of triplet excitations in a conjugated polymer containing Pt-atoms in the main chain (see Paper I), a theoretical formalism for electronic transport has been developed. It considers the interplay between polaronic distortion of the excited chain elements and disorder treated in terms of effective-medium theory. The essential parameters are the electronic coupling J, the polaronic binding energy λ that determines the activation energy of polaron motion Ea, and the variance σ of the density of states distribution controlling the incoherent hopping motion. It turns out that for the weak electronic coupling associated with triplet motion (J a few meV), the transfer is nonadiabatic. For a critical ratio of σ/Ea< 0.3, Marcus-type multiphonon transport prevails above a certain transition temperature. At lower temperatures, transport is disorder controlled consistent with the Miller-Abrahams formalism. Theoretical results are consistent with triplet transport in the Pt-polymer. Implications for charge and triplet motion in random organic semiconductors in general are discussed.