Soft x-ray spectroscopy of celestial sources with high resolving power R = E/ΔE and large collecting area addresses important science listed in the Astro2010 Decadal Survey New Worlds New Horizons, such as the growth of the large scale structure of the universe and its interaction with active galactic nuclei, the kinematics of galactic outflows, as well as coronal emission from stars and other topics. Numerous studies have shown that a transmission grating spectrometer based on lightweight critical-angle transmission (CAT) gratings can deliver R = 3000-5000 and large collecting area with high efficiency and minimal resource requirements, providing spectroscopic figures of merit at least an order of magnitude better than grating spectrometers on Chandra and XMM-Newton, as well as future calorimeter-based missions. The recently developed CAT gratings combine the advantages of transmission gratings (low mass, relaxed figure and alignment tolerances) and blazed reflection gratings (high broad band diffraction efficiency, utilization of higher diffraction orders). Their working principle based on blazing through reflection off the smooth, ultra-high aspect ratio grating bar sidewalls has previously been demonstrated on small samples with x rays. For larger gratings (area greater than 1 inch square) we developed a fabrication process for grating membranes with a hierarchy of integrated low-obscuration supports. The fabrication involves a combination of advanced lithography and highly anisotropic dry and wet etching techniques. We report on the latest fabrication results of free-standing, large-area CAT gratings with polished sidewalls and preliminary x-ray tests.