1934 Packard rear bumper disassembly

The front bumper separates in the middle and the brace is easily removed, but the rear bumper does not. What is the trick to getting it apart or putting it back together?

You don't state whether an Eight, Super Eight, or Twelve. I have very limited experience with the Twelves, but with regard to at least the Eights, it seems there were 2 types of bumpers used, the single bar and split bars joined in the center behind the center plate, and on 34 Eights I seen all the possible combinations of split both ends, solid both ends, and a mix, though of course collision repair might be a factor. My own 34 Eight is very original, a fairly early car, and has the split bumper halves front and rear. I've removed both types with no problems, if the eyes at the ends of your one-piece bumper can't simply be unthreaded and removed, I'd suspect some distortion of the bumper, the irons, or both have distorted things. The 33-36 Parts Listing doesn't seem to give any clue as to the differences in bumper type for 1934. 1933 and 35 bumpers are physically very different.