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We generalize our recent analysis of hidden-strangeness tetraquarks within the dynamical diquark model from its adiabatic form (in which each state is described solely by a diquark-antidiquark potential) to its diabatic form (which incorporates effects of dihadron thresholds upon the states). We tabulate all relevant thresholds and compute the dihadron content of each predicted state. Our results produce no particular hidden-strange tetraquark candidate whose structure is dominated by dihadron structure, in contrast to the charm sector, where many exotic states are strongly associated with such thresholds: The hidden-strange states tend to remain compact and less influenced by dihadron thresholds. Multiple states above 2 GeV with peculiar decay properties, including $\varphi \left(2170\right)$ , $f_2\left(2340\right)$ , and $\eta \left(2370\right)$ , continue to serve as excellent hidden-strange tetraquark candidates. 

The dynamical diquark model describes multiquark exotic hadrons in terms of diquark components nucleated by heavy quarks and successfully explains multiple features of hidden-charm and hidden-bottom exotics. Here, we apply the model to the marginally heavy case of hidden-strange states to probe whether mesons near 2 GeV with peculiar properties, such as $\varphi \left(2170\right)$ , $f_2\left(2340\right)$ , and $X\left(2370\right)$ , are possible tetraquark candidates. We calculate spin-multiplet average masses using potentials obtained through lattice simulations and quark models, and we also describe the detailed spectra of the expected multiplets as a diagnostic to discern the nature of future hadrons likely to be discovered in this mass region by experiments at facilities such as BESIII, JLab, and the EIC.