An exawatt-class peak-power laser architecture, based on a single, large-aperture Nd:mixed-glass amplifier combined with a technique called chirped pulse juxtaposed with beam amplification (CPJBA) is proposed to significantly extend laser capabilities beyond the present 10 PW state-of-the-art for ultra-high-intensity lasers. CPJBA utilizes a space–time coupled chirped-beam pulse to enhance the temporal compression of a fixed-aperture grating pair in a novel six-grating compressor arrangement. With this, an appropriately structured, 20-ns stretched pulse can be compressed to a transform limit of 100 fs using a maximum grating aperture of 2 m. This enables the extraction of 25 kJ of energy from a single, large-aperture Nd:glass beamline while staying below the B-integral threshold. This paper presents the numerical modeling of the various novel sub-systems required for this exawatt-class laser architecture. In particular, the unique spatial and temporal pulse distortions present during amplification using CPJBA, and the strategies used to mitigate them, are discussed.