The model-QED-operator approach [V. M. Shabaev, I. I. Tupitsyn, and V. A. Yerokhin, Phys. Rev. A 88, 012513 (2013)PLRAAN1050-294710.1103/PhysRevA.88.012513] to calculations of the radiative corrections to binding and transition energies in atomic systems is extended to the range of nuclear charges 110≤Z≤170. The self-energy part of the model operator is represented by a nonlocal potential based on diagonal and off-diagonal matrix elements of the ab initio self-energy operator with the Dirac-Coulomb wave functions. The vacuum-polarization part consists of the Uehling contribution, which is readily computed for an arbitrary nuclear-charge distribution and the Wichmann-Kroll contribution represented in terms of matrix elements similarly to the self-energy part. The performance of the method is studied by comparing the model-QED-operator predictions with the results of ab initio calculations. The model-QED operator can be conveniently incorporated in any numerical approach based on the Dirac-Coulomb-Breit Hamiltonian to account for the QED effects in a wide variety of superheavy elements.