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We demonstrate the potential of new adaptive optical technology to expand the detection horizon of gravitational-wave observatories. Achieving greater quantum-noise-limited sensitivity to spacetime strain hinges on achieving higher circulating laser power, in excess of 1MW, in conjunction with highly squeezed quantum states of light. The new technology will enable significantly higher levels of laser power and squeezing in gravitational-wave detectors, by providing high-precision, low-noise correction of limiting sources of thermal distortions directly to the core interferometer optics. In simulated projections for LIGO A#, assuming an input laser power of 125 Wand an effective injected squeezing level of 9 dB entering the interferometer, an initial concept of this technology can reduce the noise floor of the detectors by up to 20% from 200 Hz to 5 kHz, corresponding to an increment of 4 Mpc in the sky-averaged detection range for binary neutron star mergers. This work lays the foundation for one of the key technology improvements essential to fully utilize the scientific potential of the existing 4-km LIGO facilities, to observe black hole merger events past a redshift of 5, and opens a realistic pathway towards a next-generation 40-km gravitational-wave observatory in the U.S., Cosmic Explorer.