Ka-band low-Earth-orbit (LEO) downlinks can suffer second-scale reliability collapses during flare-driven ionospheric disturbances, where fixed fade margins and reactive adaptive coding and modulation (ACM) are either overly conservative or too slow. This paper presents a GNSS-free, link-internal predictive controller that senses the same downlink via a geometry-free dual-carrier phase observable at 10~Hz: a high-pass filter and template-based onset detector, followed by a four-state nearly-constant-velocity Kalman filter, estimate $Δ$VTEC and its rate, and a short look-ahead (60~s) yields an endpoint outage probability used as a risk gate to trigger one-step discrete MCS down-switch and pilot-time update with hysteresis. Evaluation uses physics-informed log replay driven by real GOES X-ray flare morphologies under a disjoint-day frozen-calibration protocol, with uncertainty reported via paired moving-block bootstrap. Across stressed 60~s windows, the controller reduces peak BLER by 25--30\% and increases goodput by 0.10--0.15~bps/Hz versus no-adaptation baselines under a unified link-level abstraction. The loop runs in $\mathcal{O}(1)$ per 0.1~s epoch (about 0.042~ms measured), making on-board implementation feasible, and scope and deployment considerations for dispersion-dominated events are discussed.