Di-lepton searches for Beyond the Standard Model (BSM) $Z^{\prime }$ bosons that rely on the analysis of the Breit-Wigner (BW) line shape are appropriate in the case of narrow resonances, but likely not sufficient in scenarios featuring $Z^{\prime }$ states with large widths. Conversely, alternative experimental strategies applicable to wide $Z^{\prime }$ resonances are much more dependent than the default bump search analyses on the modelling of QCD higher-order corrections to the production processes, for both signal and background. For heavy $Z^{\prime }$ boson searches in the di-lepton channel at the CERN Large Hadron Collider (LHC), the transverse momentum $q_T$ of the di-lepton system peaks at $q_T\lesssim {10}^{-2}{M}_{ll}$, where $M_{ll}$ is the di-lepton invariant mass. We exploit this to treat the QCD corrections by using the logarithmic resummation methods in $M_{ll}/q_T$ to all orders in the strong coupling constant ${\alpha }_s$. We carry out studies of $Z^{\prime }$ states with large width at the LHC by employing the program reSolve, which performs QCD transverse momentum resummation up to Next-to-Next-to-Leading Logarithmic (NNLL) accuracy. We consider two benchmark BSM scenarios, based on the Sequential Standard Model (SSM) and dubbed ‘SSM wide’ and ‘SSM enhanced’. We present results for the shape and size of $Z^{\prime }$ boson signals at the differential level, mapped in both cross section (σ) and Forward-Backward Asymmetry ($A_{\mathrm{FB}}$), and perform numerical investigations of the experimental sensitivity at the LHC Run 3 and High-Luminosity LHC (HL-LHC).