A numerical exploration of the linear stability of a fluid confined between two coaxial cylinders rotating independently and with an imposed axial pressure gradient (spiral Poiseuille flow) is presented. The investigation covers a wide range of experimental parameters, being focused on co-rotation situations. The exploration is made for a wide gap case in order to compare the numerical results with previous experimental data available. The competition between shear and centrifugal instability mechanisms affects the topological features of the neutral stability curves and the critical surface is observed to exhibit zeroth-order discontinuities. These curves may exhibit disconnected branches which lower the critical values of instability considerably. The same phenomenon has been reported in similar fluid flows where shear and centrifugal instability mechanisms compete. The stability analysis of the rigid-body rotation case is studied in detail and the asymptotic critical values are found to be qualitatively similar to those obtained in rotating Hagen-Poiseuille and spiral Couette flows. The results are in good agreement with the previous experimental explorations.