We study the sensitivity of top pair production with six-fermion decay at the LHC to the presence and nature of an underlying $Z'$ boson, accounting for full tree-level Standard Model $t\bar{t}$ interference, with all intermediate particles allowed off-shell. We concentrate on the lepton-plus-jets final state and simulate experimental conditions, including kinematic requirements and top quark pair reconstruction in the presence of missing transverse energy and combinatorial ambiguity in jet-top assignment. We focus on the differential mass spectra of the cross section and asymmetry observables, especially demonstrating the use of the latter in probing the coupling structure of a new neutral resonance, in addition to cases in which the asymmetry forms a complementary discovery observable.