A simple semi-analytical model for longitudinal scattering-induced attenuation and phase velocity is proposed for strongly scattering cubic polycrystals with statistically elongated grains. It is formulated by iterating the Born approximation of the far-field approximation model and by empirically increasing the coefficient in the quadratic term for the elastic scattering factor. The comparison with the three-dimensional grain-scale finite element calculations shows excellent performance of the semi-analytical model for both attenuation and phase velocity in all studied frequency ranges and especially in the Rayleigh regime in which, for strongly scattering materials, the existing analytical models significantly disagree with the numerical results.