The ability to accurately map the 3D geometry of single-molecule complexes in trace samples would lead to new insights into molecular mechanics and provide an approach for single-molecule structural proteomics. To enable this, we have developed a high-resolution force-spectroscopy method capable of measuring multiple distances between labeled sites in natively folded protein complexes. Our approach combines reconfigurable nanoscale devices we call DNA Nanoswitch Calipers, which we have previously introduced, with a force-based barcoding system to distinguish each measurement location. We demonstrate our approach by reconstructing the tetrahedral geometry of biotin-binding sites in natively folded streptavidin, with 1.5-2.5 Å agreement to previously reported structures.