Brian,
I don't use the Hornady headspace gauge so I can't speak for that process. But I can say based on my years of case forming for wildcats rounds in bolt guns, when you first start sizing a case the "headspace" distance will grow longer before you actually start shoulder bumping and pushing it back. If you put brass inside a steel die and it starts squeezing the diameter down first, that brass has to go somewhere and it grows in length. Keep screwing your die down until you get a true shoulder bump.
Military brass is tougher to do this because of the increased thickness. Plus it sounds like you are already bottomed out with your die into the shellplate. Hard to say without being there looking over your shoulder, but I have taken dies before and put the bottom end (the end that touches the shell holder/plate) on a belt sander before to take off some material. That allows your die to be screwed down a little further. This doesn't have to be an precision "cut". You just need to take some material away from the die so it will screw down further.
If this was a single stage press with a shellholder I would get the precision shell holders or simply take the top of the existing shell holder to the same belt sander and shorten it a little. It has the same effect as shortening up the base of your die. Just easier to modifiy a $4 shellholder than a $25 dollar die in case something gets messed up.
Again, I can't say this is your issue without actually being there. Do you have a single stage press to experiment with sizing on first before going to your progressive with the shellplate?
Steve