Kenstone - You're suggestion seems to have solved my problem. Many thanks!!!
I removed the pin and simply dragged and rolled the business end on a sheet of fine sandpaper and also sanded a small chamfer on the end. I then ran 6 rounds thru an empty press (no powder or primers) but did seat a bullet in each. Every single one was ejected without a primer, which is what I expected.
I also wanted to mention - to every one out there - about some parts I bought at www.titanreloading.com. They have a solution for the base of the press to keep it from having to be removed from the bench in order to get rid of the spent primers. It only works on Pro 1000's made after 1992 or 1993. Unfortunately, their web site appears to be broken at the moment or I would post the links. I think the parts are on the TITAN RELOADING Products page. (Note that I did notify them of the problem via their Contact Us page).
The parts consist of a funnel-like device that inserts into the bottom of the press, a piece of tubing that attaches to the end of the device, and optionally a cap for the end of the tube. You need to drill a hole in your bench to so that the tubing can be attached. I installed this on my Pro 1000, set up for 9mm, and it works as advertised.
Unfortunately for me my Pro 1000, set up for .357 Magnum, was made before the cutoff date and the part won't fit (the older presses have more support ribbing underneath than the new presses do).