We demonstrate efficient and economical all-solid-state post-compression based on dual-stage periodically placed thin fused silica plates driven by a more than 100 W ytterbium-doped yttrium aluminum garnet Innoslab amplifier seeded by a fiber frontend. Not only is a more than eight-fold pulse compression with 94% transmission achieved, but also the pulse quality and spatial mode are improved, which can be attributed to the compensation for the residual high-order dispersion and the spatial mode self-cleaning effect during the nonlinear process. It enables a high-power ultrafast laser source with 64 fs pulse duration, 96 W average power at 175 kHz repetition rates and good spatiotemporal quality. These results highlight that this all-solid-state post-compression can overcome the bandwidth limitation of Yb-based lasers with exceptional efficiency and mitigate the spatiotemporal degradation originating from the Innoslab amplifier and fiber frontend, which provides an efficient and economical complement for the Innoslab laser system and facilitates this robust and compact combination as a promising scheme for high-quality higher-power few-cycle laser generation.