STAR has previously reported in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV significant transverse momentum imbalance of a specific set of di-jets selected with "hard cores'', i.e. with a constituent transverse momentum cut of 2 GeV/$c$. After reclustering these same di-jets with a lower constituent cut of 200 MeV/$c$, the di-jet balance is restored to the level of p+p collisions within the original cone size of $R=0.4$. The interpretation of these results as resulting from tangential bias with restricted in-medium path lengths promises $\mathit{Jet\ Geometry\ Engineering}$ of jet production vertices through systematic variations of parameters such as centrality, the constituent $p_{T}$ cutoff, and the initial imbalance between the hard cores. In these proceedings, we present a systematic exploration of jet quenching effects on di-jets sampled from a larger parameter space and explore in detail the possibilities and limitations of using these different di-jet definitions to constrain the influence of geometry on partonic energy loss in the quark gluon plasma created in heavy-ion collisions.