This paper extends the quasi-load insensitive (QLI) Class-E Doherty power amplifier (PA) design methodology to address Doherty PA combiners with complex load impedance trajectories. Additionally, the QLI operation is analyzed for generalized class-E output matching networks with input series inductors and finite DC-feed inductors. We demonstrate that the QLI class-E Doherty operation can be achieved for various Doherty combiners by selecting the appropriate combination of class-E outputs matching network resonance factors and input series inductances. Moreover, a modified class-E output network is proposed to overcome the frequency limitation that might be caused by the class-E network resonance factor choice. To validate the proposed methodology, two 40 W Doherty PAs are designed and simulated using commercial GaN HEMT transistors achieving more than 70% efficiency over a 6 dB output power back-off at 3.8 GHz.