As a toolmaker and having worked for many years in the plastic molding industry I have polished countless dies to a high grade finish.
There is a vitally important step you are missing in the art of polishing.
Polishing is all about making scratches, making them all the same size and then just making them smaller and smaller until you can not see them.
First and most important rule is whenever you change grit size eg 400 to 600 change polish direction meaning polish across the grain of the last grit size. 90 degrees across the previous is optimal but 25 at least will still work if careful.
What this does is show up every tiny little 400 scratch that is left and it will stand out very clearly, you continue to use the current 600 grit until every scratch from the previous 400 is gone then you know every scratch on the surface is a 600 grit scratch. Go down to 800 change direction and polish out every little 600 scratch, got to 1000 change direction and polish out every 800 scratch. Do this until you finish with 1200 grit scratches any finer is not required and a waste of time unless you are making a mold for glasses lenses or something like that which must be perfect.
Buff it to a mirror like finish by getting some of the polishing soap / wax that you use on buffing wheels cut a small piece off and melt it gently in a steel can mix kerosene into it to form a paste, soak this paste into a small piece of felt and then use a wooden dowel on the felt to be like a polishing stone this will give the surface a final buff and shine it.
You will be amazed how good a polish you will get.
Remember don’t go to a finer grit till EVERY scratch is gone from the previous grit and CHANGE DIRECTION or you will never know when you have removed all the previous scratches. Oh and don’t concentrate on any one area too much or you will get a sink that will stick out like dog balls when finally buffed
Good polishing is time consuming but when done well quite satisfying.
Cheers.