We report a dynamic structure and band engineering strategy with experimental protocols to induce indirect-to-direct band gap transitions and coherently oscillating pure spin-currents in three-dimensional antiferromagnets (AFM) using selective phononic excitations. In the Mott insulator LaTiO3, we show that a photo-induced nonequilibrium phonon mode amplitude destroys the spin and orbitally degenerate ground state, reduces the band gap by 160 meV and renormalizes the carrier masses. The time scale of this process is a few hundreds of femtoseconds. Then in the hole-doped correlated metallic titanate, we show how pure spin-currents can be achieved to yield spin-polarizations exceeding those observed in classic semiconductors. Last, we demonstrate the generality of the approach by applying it to the non-orbitally degenerate AFM CaMnO3. These results advance our understanding of electron-lattice interactions in structures out-of-equilibrium and establish a rational framework for designing dynamic phases that may be exploited in ultrafast optoelectronic and optospintronic devices.