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Full disclaimer, I haven't used it before, or made a bag like that, but I don't think you need much at all to boost the structure/shape. The different thicknesses of closed cell foam are for padding and reducing impact of the cargo into the body, whereas a basket bag just needs to support itself and contents(?). I think the thinnest of the foam options (4mm?), sandwiched in, would make a very sturdy panel with loads of bounce?
You could embrace seam construction, purposefully making beefier French/bound/rolled seams to create more structure. Could also double up the fabric, and use a contact adhesive to put in support panels, exactly where you need it, minus seam allowance to make it possible to sew? And belt stiffener might be handy for specific strength - like across the base or opening.
I might be completely wrong about all this - and maybe it's combination of different techniques for different types of strength around the bag - but just some ideas.
Look forward to seeing how it turns out!
I'm planning on making a basket bag and want to give it some structure with closed cell foam. Design will be similar to a Wizard Works Alakazam or Realm Basket Bag.
Has anyone here used foam in a bag before? What thickness did you use?