We report on our re-calculation of electroweak top-quark pair production in Standard Model extensions with extra heavy neutral and charged spin-1 particles at the LHC. In particular, we allow for flavour-non-diagonal $Z'$ couplings and take into account non-resonant production in the Standard Model and beyond. As in our previous work we include NLO QCD corrections and match to parton showers with the POWHEG method fully taking into account the Standard Model and new physics interference effects. We consider the Sequential Standard Model, Topcolour model as well as the Third Family Hypercharge Model featuring non-flavour diagonal $Z'$ couplings which has been proposed to explain the anomalies in $B$ decays. Numerical results for $t\bar{t}$ cross sections at hadron colliders with $\sqrt{s}$ of up to 100 TeV are presented. We also investigate the numerical impact of the new non-resonant contributions.