Measuring the radio emission from cosmic-ray particle cascades has proven to be a very efficient method to determine their properties such as the mass composition. Efficient modeling of the radio emission from air showers is crucial in order to extract the cosmic-ray physics parameters from the measured radio emission. MGMR3D is a fast semianalytic code that calculates the complete radio footprint, i.e., intensity, polarization, and pulse shapes, for a parametrized shower-current density and can be used in a chi-square optimization to fit a given radio data. It is many orders of magnitude faster than its Monte Carlo counterparts. We provide a detailed comparative study of MGMR3D to Monte Carlo simulations, where, with improved parametrizations, the shower maximum $X_{\max }$ is found to have very strong agreement with a small dependency on the incoming zenith angle of the shower. Another interesting feature we observe with MGMR3D is sensitivity to the shape of the longitudinal profile in addition to $X_{\max }$. This is achieved by probing the distinguishable radio footprint produced by a shower having a different longitudinal profile than usual. Furthermore, for the first time, we show the results of reconstructing shower parameters for Low-Frequency Array data using MGMR3D, and obtaining a $X_{\max }$ resolution of $22g/{\mathrm{cm}}^2$ and energy resolution of 19%.