We present a signal- and reconstruction model for the radio emission of extensive air showers with zenith angles between 65$^\circ$ and 85$^\circ$ in the 30 - 80 MHz band. The model is derived from CoREAS simulations and explicitly takes into account the asymmetries introduced by the superposition of charge-excess and geomagnetic radiation as well as by early-late effects. We exploit correlations among fit parameters to reduce the dimensionality, thereby ensuring stability of the fit procedure. Our approach reaches a reconstruction efficiency near 100% with an intrinsic resolution for the reconstruction of the electromagnetic energy below 5% using a 1.5$\,$km-sparse antenna array. It can be employed in upcoming large-scale radio detection arrays using the 30-80 MHz band, in particular the Auger Radio detector of the upgraded Pierre Auger Observatory, and can likely be adapted to experiments such as GRAND operating at higher frequencies.