Single-cavity dual-combs comprise a rapidly emerging technology platform suitable for a wide range of applications like optical ranging, equivalent time sampling, and spectroscopy. However, it remains a challenging task to develop a dual-comb system that exhibits low relative frequency fluctuations to allow for comb line resolved measurements, while simultaneously offering high average power and short pulse durations. Here we combine a passively cooled and compact dual-comb solid-state oscillator with a pair of core-pumped Yb-fiber-based amplifiers in a master-oscillator power-amplifier (MOPA) architecture. The Yb:KYW oscillator operates at 250 MHz and uses polarization multiplexing for dual-comb generation. To the best of our knowledge, this is the first demonstration of a single-cavity dual-comb based on this gain material. As the pulse timing characteristics inherent to the oscillator are preserved in the amplification process, the proposed hybrid approach leverages the benefit of both the ultra-low noise solid-state laser and the advantages inherent to fiber amplifier systems such as straight-forward power scaling. The amplifier is optimized for minimal pulse broadening while still providing significant amplification and spectral broadening. We obtain around 1 W of power per output beam with pulses then compressed down to sub-90 fs using a simple grating compressor, while no pre-chirping or other dispersion management is needed. The full-width half-maximum (FWHM) of the radio-frequency comb teeth is 700 Hz for a measurement duration of 100 ms, which is much less than the typical repetition rate difference, making this passively stable source well-suited for indefinite coherent signal averaging via computational phase tracking.