The optimization of large-mode-area fiber design for the amplification of narrow-linewidth content or short pulses, susceptible to nonlinear effects, while reaching average powers exceeding the kW level is not a simple endeavor. The rapidly decreasing TMI-threshold with increasing core size leaves very little room in the 20 to 30 μm core diameter space for improved performance with respect to nonlinear effects while still delivering significant average power. We present results on a 29 μm core, polarization-maintaining LMA fiber, with a 400 μm cladding for high average power scaling. A carefully designed depressed-clad surrounds the core and enhances the bending losses for the Higher-Order Modes (HOM). Even when the fiber is loosely coiled (25 cm diameter), the filtering is very efficient which is advantageous for spreading out the fiber heat load and minimizing the effective area reduction resulting from the coiling-induced mode deformation. The fiber has been tested in a CW MOPA configuration, seeded with a longitudinally single-mode source emitting at 1064 nm, phase-modulated for Stimulated Brillouin Scattering (SBS) mitigation. The resulting slope efficiency has been measured at 88%, the PER was in the 12-15 dB range. The main feature of this fiber is its highly efficient HOM filtering capability, consequently one can maintain single mode-like operation up to the TMI threshold (slightly below 1 kW) without significant beam quality (BQ) degradation. As soon as coupling occurs between the fundamental mode and the first higher-order mode through the thermo-optic long-period grating, the energy is shed away and is coupled out in the fiber cladding.