Conducting polymers are of interest for a broad range of applications from bioelectronics to thermoelectrics. The factors that govern their complex charge transport physics include the structural disorder present in these highly doped polymer films and the Coulombic interactions between the electronic charge carriers and the dopant counterions. Previous studies have shown that at low doping levels carriers are strongly trapped in the vicinity of the counterions, while at high doping levels charge transport is not limited by Coulombic trapping, which manifests itself in the conductivity being independent of the size of the dopant counterion. Here we use a recently developed ion exchange doping method to investigate the ion size dependence of a semi-crystalline polythiophene-based model system across a wide range of conductivities. We find that the regime, in which the charge and thermoelectric transport is not or only weakly dependent on ion size, extends to surprisingly low conductivities. We explain this surprising observation by a heterogeneous doping that involves doping of the amorphous domains to high doping levels first before doping of the ordered, crystalline domains occurs. Our study provides new insights into how the thermoelectric physics of conducting polymers evolves as a function of doping level.