My finishing is not fantastic, but I work with a lot of flat
surfaces and have played about with different techniques quite a lot.
It sounds like you are using a flex shaft to do quite a bit of your
polishing, the small size of the wheels makes it quite difficult to
buff things flat with these (I use flat in a loose sense, a court
ring is fairly flat in my world, a delicate setting is not). If you
swap to a sanding stick (just tape some emery paper to a bit of wood
of about the right shape) after the filing, and take it from 400 to
1,200 then you will get rid of many of these furrows.
I’ve found that I get a bit of texture on the metal when I tumble
(some times referred to as orange peel), so I tend to tumble after
sanding and then give a quick going over with 1,200 to restore the
flat surface so that it can reflect well. Burnishing by hand instead
of tumbling can do a good job of helping a finish as well, though I
am not great at that particular technique (or I need to upgrade from
a polished bent 3 inch nail in a bit of wood I use for the purpose).
I then polish on a big (6 to 12 inch) mop whenever possible as these
give really good results, and use the flex shaft or manual polishing
to get at difficult to reach areas. A grinding motor from B and Q
will do the job, Cookson’s sell polishing spindles that will fit most
motors, so you can set this up for very little outlay, though a
proper polishing motor with good dust extraction would be a great bit
of kit to own.
For silver you can get excellent results using Hi Brite (the white
polish marketed for polishing steel, I only use this and sometimes
rouge) - it cuts much faster then Tripoli and leaves a finish not
far off of rouge. I’ve also used this on brass, copper, gold,
platinum and palladium to good effect, but I don’t have much
experience with these metals. Works wonders on steaks and hammers
too, and gives you a kind of satanic French polish.
If you want to mechanise the sanding, medium greasy on a plastic
bristle brush on your polishing motor will take off a lot metal
quickly (good for getting rid of fire stain and file scratches).
Pre-polishing can also be useful - get everything nice before final
assembly and as long as you avoid firescale (pripp’s rocks) then the
final finish is much easier to attain.
Also working by hand can be surprisingly effective. Some hi brite on
a string for threading or a bit of leather backed on wood can give
you a great finish on certain shapes. I do love my flex shaft, but
sometimes it is just not the tool for the job.