Nonresonant spectral hole burning has proven to be a versatile method to characterize the dynamics of complex fluids, including polymers. Early work focused on dielectric susceptibility measurements in glass forming liquids, while recent work from our lab used mechanical viscoelastic measurements to investigate polymer melts and solutions. While the observed results were similar, the interpretations were different, with the former being interpreted by attributing the "holes" in the response as being due to dynamic heterogeneity in the system that is related to the glass or other transition, while the latter was interpreted in a way that suggested that the observed holes depend on the type of dynamics (Rouse, terminal, etc.) rather than an identifiable spatial heterogeneity. In this work, we have expanded mechanical spectral hole burning (MSHB) into the stress-controlled domain and carried out experiments in the rubbery regime of a polystyrene solution, similar to one which was tested previously with strain-controlled MSHB. The effects of pump stress amplitude, pump frequency, and waiting time were investigated. The mechanical holes in both directions (vertical and horizontal) were successfully burned, unlike the strain-controlled MSHB experiments on the same polystyrene solution, in which vertical holes were at best incomplete. The hole intensity exhibits a linear relationship with the amount of energy dissipated in the system during the large mechanical pump modification. The results suggest that the stress-controlled MSHB can be combined with strain-controlled MSHB to build a more complete framework to investigate the dynamics of polymeric materials and is consistent with the dynamic heterogeneity being related to the type of dynamics rather than to localized heating effects.