I thought Tiger Moths were partly metal?
Nuts and bolts, cables, flying wires, engine etc. The rest is mostly wood, but the main problem is the person hours (oh, and getting a decent straight tree in the first place) Now how about a genetically modified spruce that would grow the spars to size? The twigs could do the rib sticks and so on.....
As to the fabric, could we persuade some flax plants to prepare themselves into a wing bag or four? Or shall we cheat and use dacron?
If I plant the trees now then in about forty years we could start cutting!