Despite the advantages of solution-processed organic ferroelectric transistors as synaptic components, such as stable memory states and fast switching speeds, the realization of key synaptic functions, including continuous weight modulation and low energy consumption, remains challenging. In this study, we present a strategy to optimize the charge injection barrier at the source-semiconductor interface to enhance synaptic functionalities. By incorporating heterobimetallic electrodes, we systematically tailor the hole injection barrier to suppress leakage current in the memory-off state while inducing thermionic emission-dominated channel conduction in the memory-on state. This approach enables low operating currents and facilitates the gradual modulation of channel conductance. The optimized devices exhibit a high memory on/off ratio (∼10⁴) with low off-state currents, as well as linearly tunable memory states with a low nonlinearity factor (∼1.68), making them suitable for practical hardware neural networks. Owing to these improved synaptic properties, hardware neural networks incorporating these devices demonstrate high recognition accuracy in handwritten digit classification tasks. This approach lays a foundation for the development of portable and flexible neuromorphic systems, approaching biological levels of functionality.