The author recently q-extended the approach of Qi, Wang, and Guo to derangement numbers, and successfully applied this extended approach to obtain expressions for certain types B and D of derangement polynomials as determinants of order n + 1. In this paper, we demonstrate that the q-extended approach is applicable to other generating functions, including the Eulerian polynomials A_n(t), B_n(t), and D_n(t) for types A,B, and D, as well as the types A and B "inv" analogues of q-Eulerian polynomials A_n^inv(t, q) and B_n^inv(t, q). We also present a new recurrence relation for B_n^inv(t, q).