Charge-carrier transport in a paradigmatic semicrystalline polymer semiconductor (P3HT) is important for both fundamental understanding and applications. In samples with enhanced structural disorder due to ad-hoc point defects, the mobility displays rich behavior as a function of electric field (F) and temperature (T). At low T, the mobility increases with the applied field, but upon further increasing T, the field-dependence becomes shallower. Eventually, at the highest T considered, the slope changes sign and the mobility then decreases with the field. This phenomenon can be interpreted with our model as a result of the competition between intrachain conductive-like transport (which slows on increasing F) and interchain activated transport (which is faster at higher F). The former is controlling at high T where interchain hops are strictly limited to nearest-neighbor monomers on adjacent chains. At low T, instead, interchain hops to distant sites are allowed and control the positive correlation of the mobility with the field.