I agree that the interior aluminum skin does add to the structural integrity. I, for one, have wondered just how much it adds, though. When I took my inner skins out I was suprised at how relatively few rivets were involved in holding them in. I admit to having wondered if a person could add some interior bracing using cables or straps on the diagonal instead of full sheets of aluminum.
At any rate if you would like the wood look on the inside one thing you could do would be to put aluminum in first and then use very thin plywood to keep the weight down. If you are going to cover up the aluminum I suppose that you could go with a less expensive grade. 1/8" thick plywood is available in a number of wood types at fairly reasonable prices. There are some more expensive alternatives too. You can buy thinner aircraft grade plywood. You can also buy fabric or paper backed veneer plywood that could be glued to the aluminum substrate. Check out the following sites for starters:
<-- veneer plywood
<-- all sorts of plywoods
There are other sources for aluminum listed in these forums too. Of course you could also go for the aluminum look on the inside with all new aluminum. The 2024 T3 ALCLAD that airpartsinc.com sells is the type of aluminum that is on the outside of our AS's and would be really beautiful on the inside if you like that look. It not cheap though. I think that the .025 thickness is about what you would need on the inside. The original inner skins were installed in horizontal strips by the way.
I hope all this helps at least some.