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Time-resolved atom interferometry, as employed in applications such as gravitational-wave detection and searches for ultralight dark matter, requires precise control over systematic effects. In this work, we investigate phase noise arising from shot-to-shot fluctuations in the atoms' transverse motion in the presence of the wavefront curvature of the interferometer beam, and analyze its dependence on the laser-beam geometry in long-baseline, large-momentum-transfer atom interferometers. We use a semiclassical framework to derive analytical expressions for the effective phase perturbation in position-averaged measurements and validate them using Monte Carlo simulations. Applied to 100 m and 1 km atom gradiometers representative of next-generation experiments, the model shows that configurations maximizing pulse efficiency also amplify curvature-induced phase noise, requiring micron-level control of the atom cloud's center-of-mass position and submicron-per-second control of its center-of-mass velocity to achieve sub-<inline-formula><mml:math><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> rad phase stability. Alternative beam geometries can suppress this noise by up to 2 orders of magnitude, but at the cost of reduced pulse efficiency. To address this limitation, we propose a mitigation strategy based on position-resolved phase-shift readout, which empirically learns and corrects the wavefront-induced bias from measurable quantities such as the phase-shift gradient and final cloud position. This approach restores high-sensitivity operation in the maximum-pulse-efficiency configuration without detailed beam characterization, providing a practical route toward next-generation, time-resolved atom interferometers operating at the <inline-formula><mml:math><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> rad noise level.