I used to do basically what you describe, but I've put my Thumbler Rotary and my Frankfort Vibratory out to pasture. 99% of the time, as long as brass isn't looking too dull, I'll simply ultrasonic, then use Hornady One Shot Dry Lube for my sizing lube and not worry at all about removing it.
I use a Universal Decapping die on a single stage press to deprime, then pitch everything into the Ultrasonic; let them dry overnight and then use the dry lube for sizing so I can simply load cradle to grave once I get to the press.
I use a bit of a modified version of a recipe I stole from 6mmbr.com - what they called "Clean and Shiny," which was the most expensive (but still cheap) and longest operating.
25min of 50% vinegar & water, plus a few drops of dish soap
Rinse
10min with Hornady Ultrasonic Solution in water
Rinse
10min Hot water
Rinse thoroughly in cold water
The recipe on 6mmbr uses Birchwood Casey instead of Hornady's solution, but I got 3 bottles of Hornady when I bought my Ultrasonic machine, which will last me forever. They also do 6min under solution, instead of 10, then they do 6min each of hot water then cold water. I just rinse in cold water manually after the hot water. Front to back is right at an hour per batch. Only the fewest cases will still have powder streaks baked onto the primer pocket, none of which needs to be removed, but I generally give them a quick brushing on the prep center before priming anyway.
I have a DI canister at home and a small pump, salvaged from a lab. I'll probably buy DI water once this canister is shot instead of buying another canister to replace it.
As I mentioned - I don't use a lube I have to remove, so it saves me time. I'll do a batch of brass, get them set up in the drying rack over night, then load front to back in the morning without worrying about stopping to clean the brass again.
Vibrating for hours and hours in rice or hulls with a little polish, or tumbling in stainless pins DOES get clean and bright and shiny, but they don't shoot any better or any differently than going through the Ultrasonic cleaner, and I spend a LOT less time cleaning brass. It's a bit extra hand moving, since I have to change solutions 3 times, but they are bright and clean, inside and out. No messing with rice or hulls getting packed in my 204R cases, no pins stuck in flash holes, no powdery residue...