Organic electrochemical transistors (OECTs) are a rapidly advancing technology that plays a crucial role in the development of next-generation bioelectronic devices. Recent advances in p-type/n-type organic mixed ionic-electronic conductors (OMIECs) have enabled power-efficient complementary OECT technologies for various applications, such as chemical/biological sensing, large-scale logic gates, and neuromorphic computing. However, ensuring long-term operational stability remains a significant challenge that hinders their widespread adoption. While p-type OMIECs are generally more stable than n-type OMIECs, they still face limitations, especially during prolonged operations. Here, we demonstrate that simple methylation of the pyrrole-benzothiazine-based (PBBT) ladder polymer backbone results in stable and high-performance p-type OECTs. The methylated PBBT (PBBT-Me) exhibits a 25-fold increase in OECT mobility and an impressive 36-fold increase in μC* (mobility × volumetric capacitance) compared to the non-methylated PBBT-H polymer. Combining the newly developed PBBT-Me with the ladder n-type poly(benzimidazobenzophenanthroline) (BBL), we developed complementary inverters with a record-high DC gain of 194 V V-1 and excellent stability. These state-of-the-art complementary inverters were used to demonstrate leaky integrate-and-fire type organic electrochemical neurons (LIF-OECNs) capable of biologically relevant firing frequencies of about 2 Hz and of operating continuously for up to 6.5 h. This achievement represents a significant improvement over previous results and holds great potential for developing stable bioelectronic circuits capable of in-sensor computing.