The recent development of an IFT-based Bayesian method for (near-vertical) air shower reconstruction with radio arrays in the \(30\text{-}80\,\mathrm{MHz}\) band has enabled reconstruction of the radio footprint and underlying shower parameters with an order of 1000 increase in speed as compared to the classical simulation matching approach. We present improvements to the method, including an updated parametrization of the fluence forward model and use of a Gaussian process for non-parametric contributions to the signal model. These changes increase the precision of \(X_{\mathrm{max}}\) to \(17\,\mathrm{g\,cm^{-2}}\) and in radiation energy to 6%. Additionally, the method now provides ideal coverage, without need for a calibration of uncertainties.