  We extend the investigation on jet transport coefficients within the
effective Dynamical QuasiParticle Model (DQPM) -- constructed for the
description of non-perturbative QCD phenomena of the strongly interacting
quark-gluon plasma (sQGP) in line with the lattice QCD equation-of-state -- by
accounting for inelastic $2\to 3$ reactions with gluon radiation additionally
to the elastic scattering of partons. The elastic and inelastic reactions are
calculated explicitly within leading-order Feynman diagrams with effective
propagators and vertices from the DQPM by accounting for all channels and their
interferences. We present the results for the jet transport coefficients such
as the transverse momentum transfer squared $\hat{q}$ per unit length as well
as the energy loss $\Delta E = dE/dx$ per unit length in the sQGP and
investigate their dependence on the temperature $T$ and momentum of the jet
parton depending on the choice of the strong coupling constant $\alpha_s$ in
thermal, jet parton and radiative vertices. For the latter we consider
different scenarios used in the literature and find a very strong dependence of
$\hat q$ and $\Delta E$ on the choice of $\alpha_s$. Moreover, we explore the
relation of $\hat{q}/T^3$ to the ratio of specific shear viscosity to entropy
density $\eta/s$ and show that the ratio $T^3/\hat{q}$ to $\eta/s$ has a strong
$T$ dependence -- especially when approaching to $T_c$ -- on the choice of
$\alpha_s$ in scattering vertices.
