We have investigated the magnetization and relaxation dynamics of diluted, freeze-dried superparamagnetic magnetite (Fe3O4) nanoparticle samples with organic shells using a differential fluxgate magnetorelaxometry system. The experimental data were analyzed within the framework of the moment superposition model (MSM), providing information on size and size distribution of particle cores as well as on magnetic properties such as saturation magnetization and anisotropy constant. The MSM was refined by introducing an expression for the Néel time constant depending on magnetic field, anisotropy energy, saturation magnetization, and orientation of the magnetic moment of an individual magnetic nanoparticle (MNP) with respect to the external magnetic field. It is shown that especially the dependence of the magnetization and relaxation curves on magnetizing field and magnetization time provides valuable information for an unambiguous and comprehensive determination of MNP core parameters. All experimental findings could be explained with the refined MSM; however, so far, no self-consistent parameter set was obtained quantitatively explaining all measured data. Deviations from the assumed lognormal distribution of core sizes and yet too simplified expressions for the Néel time constant are discussed as potential reasons for the observed discrepancies.