would resin or powder printing work for you?

yes, I've been thinking of using 3d printing for the lattice, but I feel like attaching the membrane to it would be an issue.

There's nothing as simple (sometimes) as replicating the physics of the real thing.  Thus: how about using balloons and fiber (printed "lace"), and perhaps freezing the result (with glue or sizing, etc) so there's no permanent air containment . . .

You could use a fishbowl air filter pump to test the pneumatic pillows. The hard part will be how you stitch together the pillows and how you hide your apparatus for air.

chicken wire and pantyhose.

what do pneumatic systems have anything to do with this?

What about making a mold out of MDF and then heating polycarbonate? You can mold the polycarbonate around the mold. When it cools, it should hold its shape.

Dont think pneumatics would work at the scale of a model. Make a mould out of foam (using milling, perhaps), and then vacuum form polycarbonate.