Several method of moments (MOM) models were developed recently to describe the evolution of soot particle populations. However, especially soot oxidation is still very challenging in MOM, as pointwise information of the underlying soot particle number density function (NDF) is usually unknown and thus, the prediction of smallest particles that oxidize completely is not easy. The recently proposed Extended Quadrature Method of Moments (EQMOM) (Yuan, Laurent, & Fox, 2012) has the potential to resolve this issue providing a continuous NDF reconstruction based on the set of transported moments. While its general suitability for soot was already demonstrated in the literature, the EQMOM moment inversion procedure reveals several numerical difficulties. In this work, we propose an EQMOM modification called split-based EQMOM that builds upon the general idea of EQMOM to represent the NDF by a weighted sum of superimposed, non-negative, continuous kernel density functions (KDFs), avoiding, however, the numerical problems of its original version. The model is based on a split of the entire NDF into a sum of overlaying density functions, whose evolution is governed by individual population balance equations (PBFs). These PBFs are derived and implemented in a novel Monte Carlo (MC) framework which is applied to simulate two fuel-rich burner-stabilized laminar premixed flames with different sooting behaviours. Results are compared to a classical MC model to demonstrate the suitability. Next, the MC data is used to assess the suitability of lognormal, gamma and inverse Gaussian distributions to approximate the NDF shape by employing the Wasserstein metric as criterion. This information is finally used to formulate an improved EQMOM soot model, which is then evaluated for both fuel-rich and oxidizing conditions. For the latter, the two-stage burner experiments of Echavarria, Jaramillo, Sarofim, & Lighty (2011) is considered, where particle oxidation is the dominant process. It is demonstrated that the proposed MOM model allows an accurate and numerically robust description of soot formation, growth and also oxidation.