  We extend and improve upon our previous calculation of electroweak top-quark
pair hadroproduction in extensions of the Standard Model with extra heavy
neutral and charged spin-1 resonances. In particular, we allow for
flavour-non-diagonal $Z'$ couplings and take into account non-resonant
production in the SM and beyond including the contributions with $t$-channel
$W$ and $W'$ bosons. All amplitudes are generated using the Recola2 package. As
in our previous work, we include NLO QCD corrections and consistently match to
parton showers with the POWHEG method fully taking into account the
interference effects between SM and new physics amplitudes. We consider the
Sequential Standard Model, the Topcolour model, as well as the Third Family
Hypercharge Model featuring non-flavour-diagonal $Z'$ couplings which has been
proposed recently to explain the anomalies in $B$ decays. We present numerical
results for $t \bar t$ cross sections at hadron colliders with a centre-of-mass
energy up to 100 TeV.
