Hybrid large mode area Ytterbium-doped double-cladding photonic crystal fibers with anti-symmetric high refractive index inclusions provide efficient amplified spontaneous emission spectral filtering. Their performances have been analyzed by numerical simulations and experimental measurements. In particular, the fiber single-mode behaviour has been studied, by taking into account the fundamental and the first higher-order mode. Two approaches, the core down-doping and the reduction of the air-hole diameter in the inner cladding, have been successfully applied to reduce the higher-order mode content, regardless of the bending of the doped fiber, without significantly affecting its spectral filtering properties.