Particle physics models with Peccei-Quinn (PQ) symmetry breaking as a consequence of supersymmetry (SUSY) breaking are attractive in that they solve the strong CP problem with a SUSY DFSZ-like axion, link the SUSY breaking and PQ breaking intermediate mass scales and can resolve the SUSY μ problem with a naturalness-required weak scale μ term whilst soft SUSY breaking terms inhabit the multi-TeV regime as required by LHC sparticle mass limits and the Higgs mass measurement. In spite of so many advantages these models have a major disadvantage in that global symmetries are incompatible with gravity and hence suffer a generic gravity spoliation problem. We present two models based on the discrete R-symmetry ZR24-which may emerge from compactification of 10-d Lorentzian spacetime in string theory-where the μ term and dangerous proton decay and R-parity violating operators are either suppressed or forbidden while a gravity-safe PQ symmetry emerges as an accidental approximate global symmetry leading to a solution to the strong CP problem and a weak- scale/natural value for the μ term. Though there are many other solutions to the μ problem, the models based on discrete R-symmetry ZR24 seem highly motivated. Such models with low μ leads to a rather clean, hadronically quiet, same-sign diboson (SSdB) signature at hadron colliders arising from neutral-plus-charged wino pair production. After imposing certain cuts we were able to get a clean signal and a 5σ reach upto mW ̃ 2 ≈ 860 GeV. It has been shown that experiments at the HL-LHC can discover the wino signal. The experimentally obtained constraints on sparticle masses have been confornted with four RNS (Radiatively-Driven Natural SUSY) models and We find that while the HL-LHC can probe considerable portions of natural SUSY parameter space in all these models, the HE-LHC will decisively cover the entire natural SUSY parameter space with better than 3% fine-tuning.