Wow. This sounds like you have been in my garage!! I started loading a couple of months ago and went through everything you described plus inconsistent COL but fortunately I've been able to work through all of it and the last 1500 rounds have been fantastic.
My biggest issue was the primer feed. If any amount of dust, powder, etc hit my slide I had to disassemble and break out the alcohol. I'm close to Dillon so I went in and described the issue and it turns out I had an old design on the primer bar. Bought my press used and I had the bar with the grooves on the bottom. The lady at Dillon gave me the current design which is completely hollow along with a new plate and I went home, installed it, and haven't touched it in the last 1000 rounds. Before that, if I got 80 rounds through it without it sticking I was lucky.
The sticking problem occasionally still happens but it's now much better. I decreased the bell so that it just gives me the minimum amount and about every 250 rounds I run just a tiny bit of lube on one case and it took 95% of the sticking away. If they start to stick again I just add another drop. Again, it's just a tiny bit of lube which is what Dillon later recommended when I was talking about another problem. I also noticed that if I add another capful of polish to the media it also helps.
The dropped primers still happen every so often and I just grab a broom when I'm done. You didn't mention OAL but I solved that by tightening down the shellplate and ensuring that my dies were all set with all stations loaded. I still get +/- .4 but it's within my range.