Thanks all – That's a nice F-104 Ramon; another prize winner no doubt?
Re oak: I also thought that solid oak would be fine, after all it's a strong, hard wood. It's not the case though. I've got some oak planks in the house left over from some Dinky Toy display cases a friend made for me, and they twist and bow like nothing I've seen.
I definitely want to stick with a wood finish; all my other paper ships are on wooden bases, although they're all different – and importantly much smaller. In hindsight I should have made them all the same style, but these things take a lot of time and I wasn't sure I'd be building more than a couple anyway. They are all 1:250 scale:




They are extremely fragile, and all have perspex cases. I specify the base size of the cases such that the wooden bases fit within them:

The model in question is the Bismarck. As Jason mentioned, a composite shelf is ideal for a temporary base to build on becasue it's dead flat and won't warp. I got one from IKEA which has what looks like a hardboard substructure (possibly with cardboard innards) and laminate surfaces:

You can probably see the relative sizes we're talking about, and the depth of that shelf is 50mm, not the absolute maximum of 30mm I'm after, and is 260mm wide, not the 200mm I want. So it's not a favourable geometry for stiffness. If I could replicate the above at 30mm deep, with a wood finish, and chamfers, I'e be perfectly happy. Doing it is a different matter though. The paper hull structure (floor, bulkheads, stiffeners, decks and sides) have formed a pretty stiff structure. It can easily be picked up at each end and won't deform to any noticeable degree – it's extremely light. However, it would not resist any warping forces at all.
I put the hidden brackets on the office wall, and the model stays there when I'm not working on it. Eventually it will be replaced by a veneered MDF sideboard I'm building (all my other office work surfaces and units are home made veneered MDF):


As I say it's absolutely critical it doesn't warp. I already scrapped the first attempt at this model after moths of work becasue of wrinkling of decks, and I couldn't live with the imperfection:

I really don't know; if this version got scrapped I would probably give up modelling altogether becasue the sheer effort needed to try and get something like this right and then have to throw it away and repeat months of work was mentally very difficult. I've salvaged models from the brink before, and as I'm sure you all know, it's not a nice feeling to see your work ruined becasue of some daft error.
How about solid wood, with a series of longitudinal slots milled in it, and metal or carbon fible strips bonded into the slots? The strips would be orientated vertically to resist bending? Whatever it is, it needs to be 100% guaranteed stable.
Cheers