I ordered a Dillon 9mm sizer die (and a hard copy of the owners manual). No dice, the same issues as before. I called in and spoke with Tim at Dillon customer service who was gruff, unhelpful, and obviously did not want to take a phone call 5 minutes before closing. After I got off the phone with him I went through the manual and verified that all the adjustments dealing with case insertion were correctly set.
The next day I spoke with Gary at customer service who felt that it might be excessive play in the shellplate due to the shellplate bolt not being tightened appropriately. I went back and checked and determined that the bolt was correctly tightened (carefully torqued down until the shellplate will not rotate and then backed off just enough until the shellplate will rotate if moved by hand). No dice, same issues as before.
Since that didn't work I pulled out my factory alignment tool and attempted to align the platform. Since I had everything apart I thoroughly cleaned and then relubed. When that was done I spent quite awhile attempting to adjust the alignment and ended up getting very frustrated. I could get the platform to line up such that alignment tool wouldn't drag in the primer hole, but only if I was pushing/applying pressure on the platform towards the front of the press. As soon as I tightened the two screws and then released my pressure the platform would come back slightly and the alignment tool would no longer smoothly align with the primer hole in the platform.
I finally noticed that if I removed the casefeed body assembly from the press the alignment tool would smoothly align with the platform. As soon as I introduced the casefeed assembly then I ran into alignment issues again. Even if I backed out the bolts on the casefeed body assembly and worked on platform alignment as soon as I went to tighten the casefeed body back up the platform wanted to hop out of alignment again. So, I called Mike (who was actually very helpful) at customer service who felt that the platform assembly may be excessively worn. My press is headed back to the factory for a refurb/overhaul.