In this paper we present numerical and experimental results revealing that the mode instability threshold of highly Yb-doped, Ce/Al co-doped pedestal fibers is affected by the size of the index-increased pedestal structure surrounding the core. An alternative preparation technology for the realization of large mode area fibers with very large Al-doped silica pedestals is introduced. Three different pedestal fiber design iterations characterized by low photodarkening were manufactured and tested in counter-pumped amplifier setups. Up to 1.9 kW continuous-wave output power of near-diffraction-limited beam quality (M2 = 1.26) was achieved with an 18/200/420 µm fiber of very low NA = 0.042, limited only by the occurrence of mode instabilities.