The photorecombination of highly charged few-electron mercury ions ${\mathrm{Hg}}^{75+}$ to ${\mathrm{Hg}}^{78+}$ has been explored with the Heidelberg electron beam ion trap. By monitoring the emitted x rays $(65--76\phantom{\rule{0.3em}{0ex}}\mathrm{keV})$ and scanning the electron beam energy $(45--54\phantom{\rule{0.3em}{0ex}}\mathrm{keV})$ over the $KLL$ dielectronic recombination (DR) region, the energies of state-selected DR resonances were determined to within $\ifmmode\pm\else\textpm\fi{}4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ (relative) and $\ifmmode\pm\else\textpm\fi{}14\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ (absolute). At this level of experimental accuracy, it becomes possible to make a detailed comparison to various theoretical approaches and methods, all of which include quantum electrodynamic (QED) effects and finite nuclear size contributions (for a $1s$ electron, these effects can be as large as 160 and $50\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, respectively). In He-like ${\mathrm{Hg}}^{78+}$, a good agreement between the experimental results and the calculations has been found. However, for the capture into Li-, Be-, and B-like ions, significant discrepancies have been observed for specific levels. The discrepancies suggest the need for further theoretical and experimental studies with other heavy ions along these isoelectronic sequences.