Electromagnetic dipole moments of short-lived particles are sensitive to physics within and beyond the Standard Model of particle physics but have not been accessible experimentally to date. To perform such measurements it has been proposed to exploit the spin precession of channeled particles in bent crystals at the LHC. Progress that enables the first measurement of charm baryon dipole moments is reported. In particular, the design and characterization on beam of silicon and germanium bent crystal prototypes, the optimization of the experimental setup, and advanced analysis techniques are discussed. Sensitivity studies show that first measurements of ${\Lambda }_c^{+}$ and ${\Xi }_c^{+}$ baryon dipole moments can be performed in two years of data taking with an experimental setup positioned upstream of the LHCb detector.