I use the HF double drum rock tumbler. I actually tried it without the SS pins while I was waiting for them to ship, and the brass got nice and shiny without them. When the pins arrived, I tried it with them and saw no significant difference in how clean they were. It was such a pain to separate them back out again, even with a magnet, that I threw the pins in a bag and they've been sitting in the garage since. I would guess primer pockets and case interiors don't get as clean without them, but in a loaded case, that's a very "out of sight, out of mind" thing for me.
Unless the brass is really nasty (like dirt/grit nasty), I just lube it up with lanolin and size/decap it dirty. My Lee dies are cheap enough to replace if this ever becomes a problem. After decapping sizing, they go in the tumbler with a little Armor All Wash & Wax, a little Lemishine, and some hot water. Anywhere from 2 hours to 8ish hours (overnight), doesn't seem to make much difference. They come out, get a good rinse, get dried off on a towel and then air dried for several hours until the insides are free of water. I live in Utah, so it doesn't usually take very long.
The Armor All seems to make the cases resist oxidation for a lot longer, weeks at least. Couldn't tell you how long they stay shiny since I don't usually have clean cases sitting around for more than a couple of weeks before they're loaded and fired again.
Oh I should mention I do all my trimming/chamfering/deburring after the brass is clean and dry.