The WIMS/PANTHER Embedded Supercell Method (ESM) provides a significant improvement in prediction accuracy in radial power distributions for pressurised water reactors compared to the standard “two-step” approach, without the need for a significant increase in computational resource. A companion paper presents validation of the ESM as previously presented, using PANTHER pin-by-pin diffusion to correct interface errors arising from the standard two-step approach. However, in principle any reference method can be used to solve the embedded supercells and correct the basic solution – this is a significant advantage of the ESM. A paper presented at PHYSOR 2016 demonstrated that use of diffusion theory introduces significant error relative to transport theory only in the high energy range, due to the discontinuous fission source when modelling the interface between two types of pincell. This paper investigates further improvement of the PANTHER solution through use of simplified PN in the fast energy groups. This solution method can be implemented without the need for any significant change to the calculation route and further improves agreement with a transport reference for a small computational cost. The remaining error in the solution is examined by derivation of an effective diffusion coefficient from a heterogeneous transport reference. This suggests a simple characterisation of the discrepancy, which can be easily corrected. Results are presented in comparison to WIMS for supercells and the KAIST benchmark. For the KAIST small core benchmark assembly power errors relative to a WIMS fine group transport reference are shown to be less than 0.5 %. Results are also presented in comparison to Monte Carlo for the Watts Bar benchmark.