Regarding the extended Huckel method (EHM) vs DFT approach, in the best case scenario the I-V curve obtained with EHM will be as accurate as the electronic structure of the system calculated using the EHM. So, you should first investigate, e.g., whether the electronic or band structure of your electrode materials and central region region is accurately given by the EHM, i.e., you should benchmark it against the DFT-calculated electronic structure. I note that this does not guarantee accurate I-V curves, as the properties of the interface between the electrode and central region system might not be described by the EHM with the DFT accuracy.