My employer once sent me to understudy a master mold polisher.This gentleman was polishing dies for striking coins at a mint while I was with him.
I cannot approach teaching you in this forum.
I can tell you the higher the polish,the more imperfections will show.I can tell you that trueness of form is critical.By using "soft" processes,you will alter trueness of form.You will make high and low spots,ripples,etc.As light hits these,the highlights will emphasize this variation,and I would prefer an as cast matte finish.
I used stones called "puddle stones".They resembled a Japanese water stone in a way.The graded grit is sifted into water and allowed to settle,then baked.
Most commercial polishing stones (Gesswein,DME) are made by a press and vitrify process,and the issue is as the stone breaks down,a chunk of 3 or 5 grits will cut diggers in the finish.
What you might try is go to a machinist suppy like MSC and order some mold finishing diamond lap compound.
Cut some pieces of hard maple to use like files.They can be formed a bit.Use the grit with the maple like a file.
If you change to a finer grit,change direction,and work till there are no scratches.
If you can settle for a soft lustre,a very fine Scotchbrite is quite forgiving,but,only as a quick finishing touch.
The greatest part of the work must be done by some form of straight tool,like a sanding block.You want to cut off the high spots while you leave the low spots alone.
I have an interesting tool called a DME "Jigger".A pistol shaped affair that makes a 0-10,000 stroke a minute reciprocal motion,controlled by a foot rheostat.It takes various stone holders and picks and laps.My little cable rotary tool is 1/2 hp 10,000 rpm with a 1/4 collet.I cut buffs with a hole saw,2 or 3 in in dia from 1 " thick rock hard felt and put them on a mandrel.I use 1 in dia Tampico end brushes.These are large enough to work flat surfaces.Holes are filled with brass plugs to not wash,etc.
Once again,have fun,but polish with something backed by wood,or a red eraser,or use polishing stones to respect the original form of the part.