We perform a detailed investigation of a Grand Unified Theory (GUT)-inspired theory of gauge-Higgs unification. Scanning the model's parameter space with adapted numerical techniques, we contrast the scenario's low energy limit with existing SM and collider search constraints. We discuss potential modifications of di-Higgs phenomenology at hadron colliders as sensitive probes of the gauge-like character of the Higgs self-interactions and find that for phenomenologically viable parameter choices modifications of the order of 20% compared to the SM cross section can be expected. While these modifications are challenging to observe at the LHC, a future 100 TeV hadron collider might be able to constrain the scenario through more precise di-Higgs measurements. We point out alternative signatures that can be employed to constrain this model in the near future.1 A SU (6)-based scenario was discussed in [30], also demonstrating that proton decay can be avoided. 2 A different variant of evolutionary algorithms, namely genetic algorithms, have been employed in the exploration of viable string theory scenarios and the pMSSM in [33,34].