Lateral overgrowth techniques have demonstrated their ability to strongly reduce the dislocation density in GaN grown on a variety of foreign substrates. The in situ deposition of SiN during metal-organic chemical-vapor phase epitaxy (MOVPE) leads to the formation of a randomly distributed mask layer and induces lateral overgrowth similar to conventional epitaxial lateral overgrowth of GaN. Specifically for GaN on silicon substrate, the insertion of SiN submonolayers is a promising method to reduce not only the dislocation density but also the tensile stress upon Si doping. Besides the advantage of uncomplicated in situ mask formation, it allows complete coalescence and planarization of the overgrown GaN within a layer thickness of about 500 nm depending on the mask thickness, thus reducing the liability to cracking. However, the insertion of ultrathin SiN interlayers and, for thicker GaN stacks, additional stress-compensating low-temperature AIN (LT-AIN) leads to a complicated interplay of stress and dislocation density. We systematically study the impact of different interlayer designs on the evolution of stress and dislocation density in GaN on Si(111). Systematic series of samples comprising different SiN coverages, consecutively increasing GaN overgrowth times, and additionally different vertical positions of the SiN interlayer with respect to the substrate and LT-AIN were prepared by MOVPE. The resulting evolution of stress and dislocation density is assessed and correlated by spatially resolved cathodoluminescence microscopy, Raman spectroscopy, and transmission electron microscopy.