The photorecombination of highly charged few-electron mercury ions Hg75+ to Hg78+ has been explored with the Heidelberg electron beam ion trap. By monitoring the emitted x rays (65-76 keV) and scanning the electron beam energy (45-54 keV) over the KLL dielectronic recombination (DR) region, the energies of state-selected DR resonances were determined to within ±4 eV (relative) and ±14 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 eV, respectively). In He-like Hg78+, 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.