I want to try to keep this topic on track, there have been some really good points made. I'll try and move this forward. For what my ultimate goal is, I really need to make a purpose built hammer. For the time being I'd like to experiment with my Little Giant. As Nuge pointed out, the last lower mandrel arrangement I showed puts a lot of overturning force on the die. I'm probably pushing the idea too far. The intent is to do hot work on these dies, hands well clear of the moving parts. I'd like to start with at least 1/4" material, probably thicker and see where I can go. The ideal progression is shown below where I would dish the center portion as Metal Mangeler described, leaving the rim unforged to contain the stretching. From there (and this would involve a purpose built hammer) I would try to draw down the rim with fullering dies to try to minimize the spreading of the overall circumference. (See diagram below)
A purpose built hammer to work the rim of a deeply dished form might look something like this crude sketch:
Knots mentioned a shrinking fixture for a pulmax. I believe he was referring to a thumbnail shrinking die as used originally on sheetmetal power hammers like this patent:
This is effective at drawing in or gathering the edge of sheetmetal to shrink the material. I've often imagined if there was an application for this in forging plate, but in my experience this type of die requires uniform behavior in the material, in other words the die works because cold sheetmetal resists and contains the portion of the "tuck" that is being compressed or shrunk.
Still brainstorming. May not build anything anytime soon, but it is fun to plan for it.
-A.