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Galaxies at redshift $z\sim 1-2$ display high star formation rates (SFRs) with elevated cold gas fractions and column densities. Simulating a self-regulated ISM in a hydrodynamical, self-consistent context, has proven challenging due to strong outflows triggered by supernova (SN) feedback. At sufficiently high gas column densities, and in the absence of magnetic fields, these outflows prevent a quasi-steady disk from forming at all. To this end, we present GHOSDT, a suite of magneto-hydrodynamical simulations that implement ISM physics at high resolution. We demonstrate the importance of magnetic pressure in the stabilization of gas-rich star-forming disks. We show that a relation between the magnetic field and gas surface density emerges naturally from our simulations. We argue that the magnetic field in the dense, star-forming gas, may be set by the SN-driven turbulent gas motions. When compared to pure hydrodynamical runs, we find that the inclusion of magnetic fields increases the cold gas fraction and reduces the disc scale height, both by up to a factor of $\sim 2$, and reduces the star formation burstiness. In dense ($n>100\;\rm{cm}^{-3}$) gas, we find steady-state magnetic field strengths of 10--40 $\mu$G, comparable to those observed in molecular clouds. Finally, we demonstrate that our simulation framework is consistent with the Ostriker & Kim (2022) Pressure Regulated Feedback Modulated Theory of star formation and stellar Feedback., Comment: Submitted to ApJ