Interesting thread. And I used to know a source where I could have as much of that sheet as I wanted - a signmaker I used to have as a customer many years ago got loads of it as packing for his raw materials. But that's years ago.
On construction, a thought that occurs to me is that you could do something like this ...
For the flow inside the sheets. Seal across the ends between the sheets, and then just box the end of the whole stack. The seals between the sheets restrict the flow to only down the internal channels.
That leaves the inter-sheet spaces sealed. When building, stop the seals a few inches short of the end - one end at one side, the other end at the other. Now form a box around the whole stack on these sections. The cell structure of the sheets will restrict the flow to between the sheets, and venting at opposite corners will force the flow to cross the sheets rather than possibly just flow down one side of the stack.
I think there are many things you could make the seals from. Someone has already mentioned silicone sealant, and did someone mention the foam draught excluder strip ? That should be reasonably strong over the sort of area involved here. Bear in mind that at least some of the seals will need to be waterproof.
And then for the connections, at the sides, this sort of thing might make a useful starting point
http://www.naplesuk.com/index/view/productDetail/category/223/product/208/Duct6-Round-to-rectangular-adaptor_white.htmespecially if you size the stack to suit direct attachment.