Next-generation radio experiments such as the radio detector of the upgraded Pierre Auger Observatory and the planned GRAND and BEACON arrays target the detection of ultra-high-energy particle air showers arriving at low elevation angles. These inclined cosmic-ray air showers develop higher in the atmosphere than vertical ones, enhancing magnetic deflections of electrons and positrons inside the cascade. We evidence two novel features in their radio emission: a new polarization pattern, consistent with a geosynchrotron emission model and a coherence loss of the radio emission, both for showers with zenith angle θ≳65° and strong enough magnetic field amplitude (typical strength of B∼50 μT). Our model is compared with both ZHAireS and CoREAS Monte Carlo simulations. Our results break the canonical description of a radio signal made of Askaryan and transverse current emission only, and provide guidelines for the detection and reconstruction strategies of next-generation experiments, including cosmic-ray or neutrino discrimination.