The two-Higgs-doublet model with a U(1)_H gauge symmetry (N2HDM-U(1)) has several advantages compared to the "standard" Z₂ version (N2HDM-Z₂): It is purely based on gauge symmetries, involves only spontaneous symmetry breaking, and is more predictive because it contains one parameter less in the Higgs potential, which further ensures CP conservation, i.e., avoiding the stringent bounds from electric dipole moments. After pointing out that a second, so far unknown version of the N2HDM-U(1) exists, we examine the phenomenological consequences for the Large Hadron Collider (LHC) of the differences in the scalar potentials. In particular, we find that while the N2HDM-Z₂ predicts suppressed branching ratios for decays into different Higgs bosons for the case of the small scalar mixing (as suggested by Higgs coupling measurements), both versions of the N2HDM-U(1) allow for sizable rates. This is particularly relevant in light of the CMS excess in resonant Higgs-pair production at around 650 GeV of a Standard Model Higgs boson subsequently decaying to photons and a new scalar with a mass of ≈90  GeV subsequently decaying to bottom quarks (i.e., compatible with the CMS and ATLAS γγ excesses at 95 GeV and ≈670  GeV). As we will show, this excess can be addressed within the N2HDM-U(1) in case of a nonminimal Yukawa sector, predicting an interesting and unavoidable Z + b^-b signal and motivating further asymmetric di-Higgs searches at the LHC.