The ground states of the positronic complexes LiPs, NaPs, e(+)Be, e(+)Mg, and of the parent ordinary-matter systems have been simulated by means of the all-electron fixed-node diffusion Monte Carlo (DMC) method. Positron affinities and positronium binding energies are computed by direct difference between the DMC energy results. LiPs was recomputed in order to test the possibility of approximating the electron-positron Coulomb potential with a model one that does not diverge for r=0, finding accurate agreement with previous DMC results. As to e(+)Be, the effect due to the near degeneracy of the 1s(2)2s(2) and 1s(2)2p(2) configurations in Be is found to be relevant also for the positron affinity, and is discussed on the basis of the change in the ionization potential and the dipole polarizability. The DMC estimate of the positron affinity of Mg, a quantity still under debate, is 0.0168(14) hartree, in close agreement with the value 0.015 612 hartree computed by Mitroy and Ryzhihk [J. Phys. B. 34, 2001 (2001)] using explicitly correlated Gaussians.