I took a look at the Aircraft Spruce site and found some interesting information. I already knew that they had a good explaination of the different types of aluminum which can be viewed at the following location:
One thing that I found in looking at the pricing for the various types of sheet was that you can buy grade 3003H-14 sheet 0.020 thick in a 4' x 12' sheet for only $39.80. I am including the description of 3003 from the above page here for reference:
This is the most widely used of all aluminum alloys. It is essentially commercially pure aluminum with the addition of manganese which increases the strength some 20% over the 1100 grade. Thus, it has all the excellent characteristics of 1100 with higher strength. It has excellent corrosion resistance. It has excellent workability and it may be deep drawn or spun, welded or brazed. It is non heat treatable. Applications: cooking utensils, decorative trim, awnings, siding, storage tanks, chemical equipment.
This stuff sounds like it would be just fine for interior use doesn't it?
I would guess that contact cement of the type used with plastic laminate counter tops would work with aluminum. The trick would be that you would only have one chance to get the positioning right. The new type, while more expensive, also no longer has the totally obnoxious oder that the older stuff had. I redid my kitchen counter tops (in my house not my AS) relatively recently and used some and was very plesently surprised about the oder. I bought a gallon of it from Lowes for something like $25 if I recall correctly. It took about 10 to 15 minutes to dry to the point of being ready to assemble and realy grabs.
Another alternative that I know would hold to aluminum is Polyurethane glue. I was trying to get stick-on wire clamp brackets to attach to the inside of my outer skin. The skin was damp and cold. The adhesive on the stick-on tabs was not sticking. I already knew that the Polyurethane glue required moisture to set so it occurred to me to try using some on the wire attachments. It does indeed stick to wet/cold aluminum. Of course this means the surface would have to be lightly misted if it was not wet. The trick is that it takes a few hours to set up. In the case of my wire tabs as long as I did not attach the wire bundles until the glue set all was well. The tabs were light enough and the glue had enough suction to stick in place - even on the ceiling - while the glue set up.
So the big question would be how to hold a sheet in place long enough for the glue to set up. That of course assumes that the new sheets would be held on only with the glue. In general most of the aluminum sheets have to be flexed to fit the curve of the inner panels where they are going to be attached. My guess is that as long as the alumuminum is stiff enough that it could be held in place at a couple of places near their mid points and the springyness of the metal would hold it in place elsewhere. Maybe a simple brace from the opposite surface (floor or wall) would work. How about something like the adjustable work support that Harbor Freight carries: