This is an appropriate SE, in my opinion. The softness of the aluminum should not be a factor, if appropriate abrasive systems are used. One starts with an abrasive grade appropriate to the worst of the scratches, despite the fact that the entire surface will be slightly eroded in the process. For localized areas, restrict the application of the abrasive as much as possible to only the affected area.
Progressing through the grits to the finest particle size will create the goal you seek. I have polished an aluminum velomobile which was badly damaged by chlorine spray. It required that I start with ScotchBrite™ abrasive pads to remove the worst of it, followed by three additionally finer grits. The end result was a mirror finish, no exaggeration.
With a softer alloy of aluminum, you'd possibly want to begin with the finest grit.
In place of, or in addition to, the grit/slurry method, consider that MicroMesh™ will provide the desired results. The typical abrasive pad is a few centimeters square and has also graduated grit levels. They are used with a water bath, to minimize scratching and to slough away the removed material. I have used these to polish 3D printed objects, also to a near-mirror shine. In the process, one of my fingernails acquired a surface shine to rival that of a high-end salon, but using water, MicroMesh™ and elbow grease alone.