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For an initial test you could simply try standing on it which (according to your calculations) will get you to 2-3 bar depending on your weight. My guess is
a) you'll need an absolute shitload of filter papers and/or coffee in there and
b) some part of it is going to fail, either the flange bits that sit on the rim of the cup or the black filter paper holder bit (depending on how you support it), or the rubber seal.
Rubber seal failure could be quite exciting, as you may end up with a high-pressure jet of boiling liquid directed at the user's face.
frankenbike
Yeah, pretty much that. I was thinking a parallel mechanism so the plunger moves roughly vertically. Aeropress slots in and I’d have the cup standing underneath, not with weight on it.
I’ve already done the CAD in Solidworks in my head.