Realistic microscale domains are an essential step towards making modern multiscale simulations more applicable to computational materials engineering. For this purpose, 3D computed tomography scans can be very expensive or technically impossible for certain materials, whereas 2D information can be easier obtained. Based on a single or three orthogonal 2D slices, the recently proposed differentiable microstructure characterization and reconstruction (DMCR) algorithm is able to reconstruct multiple plausible 3D realizations of the microstructure based on statistical descriptors, i.e., without the need for a training data set. Building upon DMCR, this work introduces a highly accurate two-stage reconstruction algorithm that refines the DMCR results under consideration of microstructure descriptors. Furthermore, the 2D-to-3D reconstruction is validated using a real computed tomography (CT) scan of a recently developed beta-Ti/TiFe alloy as well as anisotropic "bone-like" spinodoid structures. After a detailed discussion of systematic errors in the descriptor space, the reconstructed microstructures are compared to the reference in terms of the numerically obtained effective elastic and plastic properties. Together with the free accessibility of the presented algorithms in MCRpy, the excellent results in this study motivate interdisciplinary cooperation in applying numerical multiscale simulations for computational materials engineering.