The excellent idea of pressing thin but unconfined is covered in a historic arms blog (will find the link later) that has a series of detailed descriptions of C19 powder manufacture.
The factory described put thin layers of dampened powder between large copper plates, stacked up to a foot-thick deck, then put in a press.
The problem for us is that you need a VERY big press. I need 5 tons to get 3500psi for a 2-inch diameter die, checking my calcs a foot-square die calls for 150 tonnes. And it has to be delivered evenly over a large area - the upper and lower press plates would need a half-tonne of cast iron.
Just between you and me, I can't lift that even after a steak dinner!
The likely solution is as the Swiss do, a roller. The meal is still between plates, but the roller only needs to deliver a tenth the pressure. HOWEVER, you still need the press time - which needs power feed through the rollers at a very slow rate.
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Update:
The link to the pressing description
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