It seems like an effective way to go, but you have to use a wet rotary tumbler with water and dish soap.

There's enough extra work and waiting (for brass to dry) that I'd rather just stick with walnut in a vibratory tumbler.

I'm a fairly recent convert to stainless media.  I've never been able to get brass this clean by any other means.

The upside: Very clean brass, relative quiet (my design), no dust, replacement media rarely required (although you will eventually need to placed pins that are lost).

The downside: High upfront cost, need to dry brass.

Drying time really isn't an issue as I clean huge batches and dry it overnight.  I can run a dry media tumbler if I need to clean a small run of brass right away.

Hmm.  I've never used it to clean brass per se, but used it for jewellery applications to burnish brass, which makes it harder.  I'd be wondering about reduced brass life because of that.

I've used a buzz bucket for many years, but last year switched to Thumler's Tumbler, and gentlemen, there is no equal.  The brass is cleaned inside and out, including the primer pockets.  The main drawback to this method is you'll need to have access to a sink to handle the water chores.  Since drying them isn't a problem for me, I won't harp on it too much.  I wash a batch one day, and reload them the next.
A couple of tips:  Go to Home Depot and get a couple of mesh paint filters that are meant to be used on a bucket.  They have 1-gallon and 5-gallon sizes, and they're fine enough to keep the pins from running down the drain. 
If you have one of those rotary separators to sort out the dry tumbling media you use in a buzz bucket, they'll work fine for separating the pins from the brass just as well if you fill the bottom half-full of water.
An advantage for cleaning the inside of cases:  The shiny interior is easier to see when you're charging the cases with powder.  A glance down into the powder funnel and you can immediately tell if you've already dropped a charge into it.

You realize, of course, that a new user report is going to be required forthwith.     

Oh.  So I picked up the Rebel 17 kit from my OP and used it once on some 7mm brass.  Very nice brass. The only downside right now is drying time but since I don't shoot 7mm, that's not an issue.

I ended up trading 7 pounds of H1000 for the kit including media, tumbler, media separator, and Lemishine. I think I'll start cleaning all of my brass this way now.