  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.
