We investigate strong coupling topological superconductivity in twisted moiré bilayer WSe2. Our approach is based on an effective t-J model with displacement-field-dependent complex hoppings, which is treated with the variational Gutzwiller projection method. The calculated phase diagram contains domes of topologically nontrivial superconducting phases, with Chern numbers C = ±2, ±4. The order parameter is characterized by a mixed (d + id)-wave (singlet) and (p-ip)-wave (triplet) gap symmetry. We also report on the appearance of an additional topologically trivial extended s-wave and f -wave paired phases. As we show, by changing the electron density and displacement field, one can tune the singlet and triplet contributions to the pairing, as well as induce topological phase transitions between superconducting states characterized by different values of the Chern number. We analyze the physical origin of the reported effects and discuss it briefly in the view of new possibilities for designing unconventional superconductivity in moiré systems.