We present the results from a pair of high-resolution, long-timescale ($\sim10^5~{\rm GM/c^3}$), global, three-dimensional magnetohydrodynamical accretion disk simulations with differing initial magnetic plasma $\beta$ in order to study the effects of the initial toroidal field strength on the production of a large-scale poloidal field. We initialize our disks in approximate equilibrium with purely toroidal magnetic fields of strength $\beta_0$ = 5 and 200. We also perform a limited resolution study. We find that simulations of differing field strengths diverge early in their evolution and remain distinct over the time studied, indicating that the initial magnetic conditions leave a persistent imprint in our simulations. Neither simulation enters the magnetically arrested disk regime. Both simulations are able to produce poloidal fields from initially toroidal fields, with the $\beta_0$ = 5 simulation evolving clear signs of a large-scale poloidal field. We make a cautionary note that computational artifacts in the form of large-scale vortices may be introduced in the combination of initially weak field and disk-internal mesh refinement boundaries, as evidenced by the production of an m = 1 mode overdensity in the weak field simulation. Our results demonstrate that the initial toroidal field strength plays a vital role in the simulated disk evolution for the models studied.