Precision measurements of time-reversal (T) symmetry violating moments probe physics beyond the Standard Model. We show that precision spectroscopy of paramagnetic lanthanide and actinide ions doped into noncentrosymmetric crystals can extend the sensitivity of searches for T-violation in nuclear physics. The unpaired valence electron in these ions allows the engineering of highly-coherent hyperfine transitions that are insensitive to magnetic fields, yet highly sensitive to new physics. These systems also provide other advantages for new physics searches, including large numbers of ions that can be measured in doped crystals, strong electric polarization of the ions by the crystal fields, enhancement of T-violating nuclear moments in nonspherical nuclei, and accurate comagnetometers generated by crystal symmetry. We estimate the new physics sensitivity of these proposed systems to be two orders of magnitude better than existing constraints.