I use a Thumbler's Tumbler and wash 1000 cases at a time as well. My brass is not deprimed at this point. I use brass pins instead of SS. I drain the water and rinse. I then use the Berry's Brass Pan Sifter to get the pins out. I pour about 250 out at a time and shake around until all of the pins are out. Sometimes the pins fly around when I am shaking them out, however after 75,000 rounds, I have never had a pin make it to the reloader. I was about to try a rotating separator, however after this thread I may stick with my current method.
I usually let mine dry for two days. Once I was drying 45acp and thought they were dry after 1 day, I reloaded them and 2 or 3 out of a hundred would not go bang - water in the primer holes. Now, I wait at least 2 days and sometimes use a fan.