The combination of multi-band imaging from the Hubble Space Telescope with Multi-Unit Spectroscopic Explorer integral field spectroscopy, obtained at the Very Large Telescope, has recently driven remarkable progress in strong lensing (SL) modeling of galaxy clusters. From a few tens of multiple images with photometric redshifts per cluster, a new generation of high-precision SL models have recently been developed, by exploiting in some cases over a hundred of spectroscopically confirmed multiple images and cluster member galaxies. A further step forward is expected with James Webb Space Telescope observations of SL clusters (from hundreds to possibly a thousand of multiple images). In this context, we present a new, state-of-the-art SL model of the galaxy cluster MACS J0416.1-2403, utilizing 237 spectroscopically confirmed multiple images, which is the largest sample of secure multiply lensed sources utilized to date. In addition, this model incorporates stellar kinematics information of 64 cluster galaxies and the hot-gas mass distribution of the cluster, determined from Chandra X-ray observations. The observed positions of the many multiple images are reproduced with a remarkable average accuracy of 0.43". To further assess the reliability of this lens model and to highlight the improvement over previously published models, we show the extended surface brightness reconstruction of several lensed galaxies through a newly developed forward modeling software. The comparison with other SL models of the same cluster demonstrates that this new model is better suited to accurately reproduce the positions, shapes and fluxes of the observed multiple images. Besides a robust characterization of the total mass distribution of the cluster, our model can provide accurate and precise magnification maps that are key to studying the intrinsic physical properties of faint, high-redshift lensed sources. The model is made publicly available through our newly developed Strong Lensing Online Tool (or SLOT), that thank to a simple graphical interface allows astronomers (including lensing non-experts) to take full advantage of the predictive power of the model, including statistical uncertainties on the relevant quantities associated to the multiply lensed sources.