Electron-impact ionization of neutral neon continues to be of interest both from a fundamental and an applied perspective. Non-perturbative calculations are required for the electron-impact ionization of ground and excited states of neon. R-matrix with pseudostates (RMPS) calculations for the electron-impact ionization of the 1s²2s²2p⁶ ground state of Ne at higher incident electron energies are now made possible by the further partitioning of each individual LS partial wave across a greater number of processors. Furthermore, instead of a long sequence of parallel matrix diagonalizations, every partial wave diagonalization is now carried out concurrently. The ground-state cross section is found to be in excellent agreement with recent experimental measurements. The previous work of Ballance et al (2004 J. Phys. B: At. Mol. Opt. Phys. 37 4779), for the ionization of the 1s²2s²2p⁵3s excited state of Ne, has been extended to examine the ionization of the 1s²2s²2p⁵4s and 1s²2s²2p⁵5s excited states. Very good agreement is found between R-matrix with pseudostates and time-dependent close-coupling calculations for the 1s²2s²2p⁵4s excited state. The non-perturbative cross sections for low nl are used to scale semi-classical impact parameter cross sections to high nl. Ionization cross sections for the ground and all excited states will enable the accurate determination of the generalized collisional-radiative ionization rate coefficient for neutral Ne in finite plasmas.