Low-frequency quasi-2D plasma convection and the resultant nondiffusive cross-field plasma transport in mirror-based systems are studied by means of direct computer simulations of nonlinear plasma dynamics in a frame of adiabatically reduced one-fluid MHD model. The simulations were performed for axisymmetric or effectively symmetrized paraxial mirror-based systems such as tandem mirror and gas dynamic traps. Various regimes of plasma confinement with sheared plasma rotation were modeled and analyzed. Simulations have shown formation of large-scale flute-like stochastic vortex structures, which are similar to the vortex-like structures observed in GAMMA 10 and GDT experiments. It was shown that a controlled formation of high-vorticity layers allows one to prevent fast plasma degradation and to reduce considerably the nondiffusive cross-field plasma transport even in a presence of unstable pressure driven modes with a weak MHD drive. The effect results from an appreciable nonlinear modification of dominant vortex-like structures due to a competition between pressure driven and Kelvin-Helmholtz instabilities.