Ytterbium-doped solid-core photonic bandgap fiber amplifiers operating at the long-wavelength edge of the ytterbium gain band are reported. The low-loss bandgap transmission window is formed in the very low gain region, whilst outside the bandgap, large attenuation inhibits the exponential growth of amplified spontaneous emission in the huge-gain 1030-1100 nm region. Hence parasitic-lasing-free, high-power amplification with a marked efficiency is enabled. A 32 W output at 1156 nm with a 66% slope efficiency and 30 W output at 1178 nm with a 58% slope efficiency were successfully obtained. To our knowledge, these are the highest output powers generating from active photonic bandgap fibers, as well as from ytterbium-doped fiber lasers at these wavelengths.