We report on an ytterbium doped single mode distributed mode filtering rod fiber in an amplifier configuration delivering high average output power, up to 292 watts, using a mode-locked 30ps source at 1032nm with good power conversion efficiency. We study the modal stability of the output beam at high average output power levels and demonstrate a 44% power improvement before the threshold-like onset of mode instabilities by operating the rod fiber in a leaky waveguide regime. We investigate the guiding dynamics of the rod fiber and explain the improved performance by thermally induced refractive index profile change.