I use a large Harbor Freight cement mixer (my buddy gave it to me, it was new, but I know I could need a new motor or belt at any time). I have ~60lbs. of pins in there I guess, and I use water (I try to start with boiling water) dish soap, I have some kind of lemon soap, and lemonshine. I guess I need to get more of that come to think of it. After tumbling for half and hour or so, I start to dump the water and rinse it and do that a few times until it's clean, no soap. Then the brass comes out and I shake out the pins (I've been doing .50BMG so I guess some thing will be different with smaller cases) and put 'em in a Dillon separator basket and spin it to remove as much water and any pins that may come out. Then they go in the back yard, during the warm weather, and on a ~2x8 foot frame with 4' legs and quarter inch screen stapled to the bottom of the frame. The whole rack dries completely on a warm day. Winter I try other methods.
It works well, the only problem is if you clean again after sizing. I decap dirty brass, then clean, then size, trim, etc., then clean again, then prime and load. The decapped brass is super clean. Like brand new clean. The sized brass? dull and dirty.
The lube sticks to the brass and so does the dirt. There are ways to fix this, like maybe a dunk in parts cleaner before going in the mixer. Something to dissolve the case lube. It's on my pins now so I need to clean those. It's not enough to make me not do it anymore, nothing else is faster and does a good job. But I do have to come up with a solution for easily removing the case lube.
For precision brass, I don't wanna run that in a big cement mixer. You can see what it does to the brass. It's nothing bad really, but it's nothing you wanna do to precision brass. Only way I know to put it, if you use one then you'll understand. For bulk brass it's a godsend. If you load .50 BMG and belt it, there's no other way to clean 10k pieces that I know of. So I have a Hornady ultrasonic cleaner I got for a really good deal. It holds a full M4 upper and has a basket to hold brass, etc. It'll hold a good bit of brass if we're not talking BMG. It'll hold a fair amount even if we are. But you can clean hundreds of .308 Lapua cases in it no problem and not do any damage and clean completely inside and out.
I'd ultrasonic everything if I could. It's almost like magic how fast and how easy and how efficient that damn thing is. But you have to know how it works or you can damage or even destroy some parts. If you can get away with one of those, if that suits your needs, do that. Ultrasonic, forget the pins, forget the tumbler (though I keep a tumbler to polish loaded ammo sometimes, carefully). Instead of Hornady, look around first, I spoke to an US guy here in WA and he said you can get bigger US cleaners for decent prices used. To look around, call around. They're pretty simple actually. A US cleaner will both do a better job and do it without even touching the brass, so no damage like tumbling, wet or dry.
In fact, the only reason I have that mixer and pins and wet tumble is because I have two 55gal. drums of .50 BMG brass I gotta decap, clean, size, clean and load. The local US cleaner wanted $1000 to clean 'em once. Not doing that twice, so here I am. But I US clean my Lapua brass, my Grendel brass, hell, any lot of brass that'll fit in the US cleaner.
Good luck whichever way you go. I kinda hope you don't need the wet tumbler because it means you're dealing with the same problem I am, in one way or another, and it sucks. Hoping a US cleaner can meet your needs, a good low cost industrial model.