You might check into a jeweler's flat lap -- it's a machine designed
specifically to polish and buff flat surfaces. The only issue might be
finding a lap big enough to take your pieces -- the typical bench-top
lap has a 6 or 8 inch diameter disk, so the size that you can work on
is limited.

A lap's polishing wheel is a hard felt tapered edge disk, cut with
several slots. You hold the work underneath so you can see what you
are doing -- the rotation causes the slots to make the disk
"transparent", so you can see through it.

Generally, they are used for polishing and buffing after the work is
already sanded to about 600 grit. You could maybe use one for sanding
by using a coarser grit compound on the disk, but I've never tried it
that way. You can certainly polish and buff flats without compromising
the surface, though.

Here's a picture of one:
http://www.gesswein.com/catalog/cata...TOKEN=32490561

Regards,

Bob