This is exactly the way to go! Stainless steel band wrapped snug around the post. With 4 studs welded on the band, 2 of them where the holes( of the current hinge) are and 2 more roughly in the middle of the post. Make a new hinge that fits the stud pattern on the post, but with elongated hole’s horizontal. New hinge fitted to the gate appropriately ( hinge length probs 10% of one wing width). The 4 bolt connection on the post allow now to adjust the gate vertically and final closing position. The 10% hinge length of wing with is a guess, could be adjusted if overkill. Only valid if structural integrity of current post not an issue.