Turbulent dynamo theories have faced difficulties in obtaining evolution of large-scale magnetic fields on short dynamical time-scales due to the constraint imposed by magnetic helicity balance. This has critical implications for understanding the large-scale magnetic field evolution in astrophysical systems like the Sun, stars and galaxies. Direct numerical simulations (DNS) in the past with isotropically forced helical turbulence have shown that large-scale dynamo saturation time-scales are dependent on the magnetic Reynolds number (Rm). In this work, we have carried out periodic box DNS of helically forced turbulence leading to a large-scale dynamo with two kinds of forcing function, an isotropic one based on that used in PENCIL-CODE and an anisotropic one based on Galloway-Proctor flows. We show that when the turbulence is forced anisotropically, the nonlinear (saturation) behaviour of the large-scale dynamo is only weakly dependent on Rm. In fact the magnetic helicity evolution on small and large scales in the anisotropic case is distinctly different from that in the isotropic case. This result possibly holds promise for the alleviation of important issues like catastrophic quenching.