The top and bottom electrodes of the ferromagnetic manganite La_0.7Ca_0.3MnO₃ may be magnetically decoupled by a La_0.59Ca_0.41MnO₃ interlayer in which ferromagnetic and paramagnetic phases coexist. In mesas fabricated from these trilayer films, in-plane magnetic domain walls associated with the antiparallel magnetic electrode configuration show a giant resistance-area product >10^-10 Ωm². This is almost two orders of magnitude larger than our devices with interlayer composition La_0.6Ca_0.4MnO₃ [C. Israel et al., Phys. Rev. B 78, 054409 (2008)] where phase separation is less extreme. High-field treatments modify the ferromagnetic phase fraction of the interlayer.