Thanks again for everyone's help. Here, the PMs, the email and the couple of phone calls. Like I said, best folks on the planet.
During the day yesterday, I got to thinking that the arm might be coming in contact with two of the three washers used in mounting the press to my bench. Large diameter, but thin washers extending beyond the edge of the bottom side of the bench. What can I say? I mounted it when I first moved to the house and didn't have my miscellaneous screws, nuts and washers collection built back up...gave them away when I moved from Alabama.
Sure enough, they were contacting the arm of the press. I replaced them with smaller washers that don't impede the arm. Things suddenly got a lot better. I don't feel mush at the bottom any more. I only did 5 cases, still need to do a better sample, but I feel a LOT better about it. In retrospect, as Wilbur pointed out, it was pretty obvious. If I hadn't been on the phone with Vargetman, I'd have slapped my head and and said "Doh!".
I'm looking into replacing the Lee press next month. My fun money account is BARE right now from the college recruiting trips with my daughter...and the A/C going out while on the trip...
Also, with that said, I talked Ezell into building a little fixture with dial indicator to help me measure bump. It'll be a help.