Utilizing the excellent mass resolving power of SHIPTRAP and the charged-particle-$\gamma$ multicoincidence setup TASISpec, the decay path of the $^{213}$Ra ground state can be exclusively studied. Based on virtual experiments with Geant4 it is possible to refine the $\alpha$-branching ratios of the $^{213}$Ra ground state as well as $\gamma$-ray branching ratios in the $^{209}$Rn daughter. The present study provides a proof of concept where clean quantum-state selective particle-$\gamma$ decay spectroscopy is used in conjunction with detailed Geant4 Monte-Carlo simulations to gain insight into nuclear structure properties.