Does the charge-transfer gap set the maximum $T_{c}$ across cuprate families?

For hole-doped cuprates at optimal doping, test whether $T_c,\mathrm{max}$ and the zero-temperature pair density decrease monotonically with the charge-transfer energy $\Delta_{\mathrm{CT}}$ (equivalently increase with $J\sim t_{\mathrm{pd}}^4/\Delta_{\mathrm{CT}}^3$), as superexchange pairing in the three-band Emery model predicts. An answer is a cross-family data set ($\Delta_{\mathrm{CT}}$ from optics or tunneling, $T_c,\mathrm{max}$, superfluid density) with a quantitative fit to model predictions, or a counterexample family.

Measurement of $\Delta_{\mathrm{CT}}$ and the pair or superfluid density in at least five cuprate families, compared with three-band model calculations of $T_{c}$ versus $\Delta_{\mathrm{CT}}$.