We model energetic particle injections during substorms by investigating the particle interaction with an earthward propagating electromagnetic pulse of spatially localized transient electric (E) and magnetic (B) fields, superposed over a background B field. The current work extends our previous model by considering the background field to be nondipolar (stretched) before the arrival of the pulse (i.e., during the substorm growth phase), changing in a time-dependent manner into a dipole field in the wake of the pulse. The particle motion still conserves the first adiabatic invariant, even in the stretched B field, and both protons and electrons are convected earthward by the E ¿ B drift to regions of higher field, undergoing betatron acceleration. As in the previous model, we find fully analytical solutions for the gyrocenter motion of the 90¿ pitch angle particles, and we use them to compute the injected particle flux. We discuss how the model can explain several injection features such as the low/high energy cutoffs, and finally we apply the solutions to a simulation of an actual injection event, obtaining good agreement with observations. The current results with the more realistic background field show significant increase in particle flux for substorm energies (tens to hundreds of keVs) compared with the case of a dipole background, leading to the conclusion that the particles have to arrive from closer to Earth than before in order to explain the observed injected flux levels. The new model provides a better fit to observations than the previous one, since it requires lower transient E fields (more realistic of a typical substorm), and thus better explains the ubiquity of particle injections associated with substorms.