We present a new high-precision, JWST-based, strong-lensing model for the galaxy cluster Abell 2744 at z=0.3072. By combining the deep, high-resolution JWST imaging from the Grism Lens Amplified Survey from Space-JWST and Ultradeep NIRSpec and NIRCam Observations before the Epoch of Reionization programs and a Director's Discretionary Time program, with newly obtained Very Large Telescope/Multi Unit Spectroscopic Explorer (MUSE) data, we identify 32 multiple images from 11 background sources lensed by two external subclusters at distances of ~160" from the main cluster. The new MUSE observations enable the first spectroscopic confirmation of a multiple-image system in the external clumps. Moreover, the reanalysis of the spectrophotometric archival and JWST data yields 27 additional multiple images in the main cluster. The new lens model is constrained by 149 multiple images (~66% more than in our previous model) covering an extended redshift range between 1.03 and 9.76. The subhalo mass component of the cluster includes 177 member galaxies down to mF160W=21, of which 163 are spectroscopically confirmed. Internal velocity dispersions are measured for 85 members. The new lens model is characterized by a remarkably low scatter between the predicted and observed positions of the multiple images (0.43"). This precision is unprecedented given the large multiple-image sample, the complexity of the cluster mass distribution, and the large modeled area. The improved precision and resolution of the cluster total mass distribution provides a robust magnification map over a ~30arcmin^2^ area, which is critical for inferring the intrinsic physical properties of the highly magnified, high-z sources. The lens model and the new MUSE redshift catalog are released with this publication.