...the bent primer rod that activates the primer shuttle still comes out of the press at the bottom of the press.
You do not have the press setup correctly.
The end of that rod is threaded and there is a nut that screws on the end ot the rod to hold it in place. The nut on the top is used to tighten and hold in place the primer guide rod. Untill you fix that you will continue to have issues.
I know most of the problems with this press so I also suggest you have an extra primer gulde. primer rams. springs for the plate, springs for the other parts. a set of allen wrenches for adjustments, The top piece plastic piece for the primer guide, and anyt other small part I forgot to mention.
Hornady tech support is really good for part replacment but without spares on hand you are down for several days. As an example I broke two springs on one night.