The determination of the color force in a quark-gluon plasma (QGP) is a key objective in the investigation of strong-interaction matter. Open and hidden heavy-flavor observables in heavy-ion collisions (HICs) are believed to provide insights into this problem by comparing calculations of heavy-quark (HQ) and quarkonium transport with pertinent experimental data. In this work, we utilize the $T$-matrix formalism to compute charm-quark transport coefficients for various input potentials previously extracted from simultaneous fits to lattice-QCD data for HQ free energies, quarkonium correlators and the QGP equation of state. We investigate the impact of off-shell effects (spectral functions) in the QGP medium on the HQ transport, and compare to earlier results using the free or internal HQ energies as potential proxies. We then employ the transport coefficients in relativistic Langevin simulations for HICs to test the sensitivity of heavy-flavor observables to the HQ interactions in the QGP. We find that a strongly-coupled $T$-matrix solution generates a HQ elliptic flow comparable to the results from the internal energy at low momentum, driven by a long-range remnant of the confining force, while falling off stronger with increasing 3-momentum. The weakly coupled $T$-matrix solution, whose underlying potential is close to the free energy, leads to an elliptic flow well below the experimentally observed range.
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