The result is a rotated, ballooned image, but with every star at its correct coordinate. Now you see the need for some white surround working area. Read into Photoshop as separate layers. Create visibility masks. Their centerlines are equivalent, just adjust horizontally until the stars line up.
Color adjust each layer to hide the center of the seam.
Make layer color adjustments until the seam as it crosses the centerline becomes invisible. The seam may become visible at the edges, but that will be addressed next. Localized color adjustments, each layer, to hide remainder of seam. This takes some practice and judgement. Select a region of a layer, make a small color adjustment, select a smaller region, make another small adjustment, continue until the seam edge is invisible with the next layer.