While I would prefer to have the Lee Classic cast iron Turret press, I have the same as you.
Primer seating works perfectly well. At least 60K cases processed.
I've done three different methods to stop the spent primer problem and leaves the arm in place. All three worked "MOSTLY".
1. A heated and bent piece of 2" wide plexiglass that walled in the back and right side of the press. It was held in place by being "sprung" betwween the three posts supporting the turret. Simple in/out. Primers fell into the holes and accumulated under the press. (SOME didn't fall into the press openings.)
2 A small aluminum shute on the right side of the press to divert spent primers to a box beside the press. (some landed and stayed on top of the base and had to be pushed into the shute by hand.)
3 Like the post above, I put a cardboard wall on the right side to divert spent primers into the openings on the press base.. I cut a funnel-shaped hole in the wood under the press base, so the spent primers would end up in a catch underneath the benchtop.
All of these helped substantially, but still didn't eliminate the occassional irritations. I now clean cases, size and deprime on a LEE Reloader single stage on my patio. I tumble and reload in the garage. No more primer problems. My Turret press doesn't get dirty and seldom needs cleaning/oiling.
Good luck