Resonant slow extraction from the CERN Super Proton Synchrotron (SPS) is performed operationally with the constant-optics slow-extraction (COSE) scheme, in which, instead of sweeping the betatron tune across the resonance, the entire machine follows the momentum of the extracted beam slice, so that the extraction optics remain constant throughout the spill. The constant separatrix improves the quality of the extracted beam and underpins the loss-reduction schemes on which the planned Beam Dump Facility (BDF/SHiP) depends. The scheme, however, requires every magnet, in the ring and in the transfer lines alike, to track the programmed momentum sweep. While the laminated ring magnets follow it readily, the MSSB splitter magnets of the North Area transfer lines are built with massive solid steel yokes. The limiting phenomenon is the rate-dependent screening by eddy currents in the yoke bulk, which attenuates and delays any programmed field change to such an extent that a current program computed without pre-distortion delivers only 54% of the demanded field modulation. We characterize the magnet in the laboratory as a dynamic plant, harmonic by harmonic, and apply feed-forward pre-distortion of the current through the inverse of the measured plant, refined by a single iterative-learning correction. The method is applicable to programmed field modulation in any solid-yoke magnet.