I finally found some .45 Auto Rim brass at a local gun show at a price I was OK with. Now I need a shellholder.
My press is a 50-plus year old Lyman All-American turret press that is designed to take the old-style shellholder with a cylindrical extension that fits into a hole in the ram, and gets anchored in place with a set screw. I never felt any overwhelming desire to update my press. It does everything I need and I have nearly all the original-style shellholders I need for it (just not one for the Auto Rim).
Ideally I would like to find one of these old-style shellholders, but I realize this is going to be a pretty long shot.
I do have an adapter that accepts the more common snap-in shellholders and one of the modern ones would be OK, too.