OP, you're not alone. The primer system is one of the "soft" points of the Evo/Pro. It's basically a beefed-up version of the 1050 priming system, but it seems to have the same weaknesses. Also, the Evo is a highly-engineered but exquisitely sensitive machine that needs a lot of fine adjustments to keep it running. I've found that the stacked priming system and case feed system (case feed assembly + shell plate) are common causes of stoppages. Sometimes it runs fine, sometimes it can't do 100 rounds without stopping. And yes, I've followed every bit of advice from M7, their manuals and handouts, the M7 Community (which is pretty sparse), and here at BE, and put countless hours into making it run.
With the primer system, it's crucial to check the alignment of the primer tube over the primer pocket in the shuttle, adjustment of the primer shuttle's stop point in its travel backward (to align it properly with the shuttle pocket), and making sure the downward end of the internal primer tube and the shuttle pocket are smooth and with no rough edges. The lower end of the primer tube gets chopped up over time due to wayward movements of primers and screws up the smooth delivery of primers into the pocket.
You need to take the primer feed ass'y off at intervals and clean everything to keep grit out of it. Oil the sides of the shuttle lightly, per the instructions.
There doesn't seem to be any way to keep primers from flipping out of the shuttle and getting crushed between the shell plate and the primer tube flange, even with a protective plastic plate over the gap between them or at the aft end of the shuttle (just like the 1050...).
It will also fail to feed primers at regular intervals. A Primer Orientation Sensor helps keep the mess down by stopping the machine.
It also "smears" primers fairly regularly, perhaps because the primer seating rod gets stuck in the large hole at the front of the shuttle. That needs to be smoothed and polished.
You might need to keep the production rate at 2000 RPH or less. The shuttle moves pretty fast at any speed, and the faster you cycle the more likely things will go wrong.
None of this is new. Many folks have had these problems; it seems "built in" to the design. They're apparently working on a new primer feed design; that may be the Evo-version primer collator that we've heard about (not out yet).
Best of luck with your Evo Pro. It can be an adventure!