You can create a "hat board" by taking two square pieces of cardboard and cutting a hole in one to match the crown diameter.
Cover both "insides" of the cardboard squares with wax paper, cellophane, or aluminum foil.
Steam the hat brim very well off the stove with the "War Departments" tea kettle. Do this when she's out shopping so she doesn't know/object to what you are doing with her kettle...and the noise.
When still wet from steaming, place the "Cover" (as us Marines call it) inside the two pieces of cardboard with the inner covering of material to keep the cardboard from adhering to the wet hat. Clamp it shut with bricks, tape, big paper clips, etc., anything that will hold it TIGHT in place.
Take the hat to a "hide-away" so that the War Department doesn't ask, "What is that?" And then follows up with, "How did you do that?' Because then she will say, "YOU DID WHAT WITH MY TEA-KETTLE...ON MY STOVE!!"
The next day go to the hide-away and remove your hat. It will be stiff enough to once again get in the face of a "boot" and whack his forehead with the brim!
You could probably do this ONCE with the War Department as a joke!