I deprime using an universal depriming die, so I don't get my real dies dirty or scratch them. Even if it does scratch the depriming die, it's not really expensive compared to high quality resizing dies. Then I tumble. Wet tumbling with stainless steel. Not having the primer there makes drying a lot faster and easier.
I know a wet tumbler costs like 3X as much, but then media is reusable and it does a much, much cleaner job than walnut or corncub.
Dry tumblers also project a lot of fine dirth in the air. So unless you do it outside or in a garage or somewhere you don't mind having a lot of fine particle (aka dust), wet tumbling is much better. Never tried an ultrasonic cleaner, but from the top of my head I'd go ultrasonic before I'd go the dry tumbling route.
Removing all the stuck media from flasholes would rive me nut. Tumbling for 4-6 hours compared to 1-3 hours with wet tumbling is too long. To each their own, but personnaly, I would never get into dry tumbling; that's just too much work. Compare it to washing anything in your life: clothes, yourself, whatever. How many of those thing would you attempt to wash without water? Personnaly, none.
Anyway, that's not what you asked, but here it is:
1-Deprime (using universal depriming die);
2-Tumble;
3-Dry;
4-Congratulation, you've just got clean unprimed cases, go on with your usual reloading technique.
I guess if you use a dedicated single stage press with an universal depriming die to deprime (or Frankford depriming device, if it works well, I really don't know if it does), you could use the same method without much problem even with dry tumbling. Make sure you keep the depriming pin on your resizer so it pushes out stuck media, and you should be good to go.