Jet-medium interactions are studied via a multi-hadron correlation technique (called "2+1"), where a pair of back-to-back hadron triggers with large transverse momentum is used as a proxy for a di-jet. This work extends the previous analysis for nearly-symmetric trigger pairs with the highest momentum threshold of trigger hadron of 5 GeV/$c$ with the new calorimeter-based triggers with energy thresholds of up to 10 GeV and above. The distributions of associated hadrons are studied in terms of correlation shapes and per-trigger yields on each trigger side. In contrast with di-hadron correlation results with single triggers, the associated hadron distributions for back-to-back triggers from central Au+Au data at $\sqrt{s_{NN}}$=200 GeV show no strong modifications compared to d+Au data at the same energy. An imbalance in the total transverse momentum between hadrons attributed to the near-side and away-side of jet-like peaks is observed. The relative imbalance in the Au+Au measurement with respect to d+Au reference is found to increase with the asymmetry of the trigger pair, consistent with expectation from medium-induced energy loss effects. In addition, this relative total transverse momentum imbalance is found to decrease for softer associated hadrons. Such evolution indicates the energy missing at higher associated momenta is converted into softer hadrons.