Originally Posted by wraub
Also, wouldn't reducing it to a proper thickness likely remove some/all of the plies in the process?
Yes and no.
If You use regular plywood, yes, you'll be left with one or two layers, and depending on the original thickness and number of plies it'll probably warp more or less.
The plywood to use though, if You have to buy it that is, is aircraft grade plywood that is made of very thin plies, so you may succeed in thinning it if you can't find 2-3mm thick material that can be used as-is.
As You can imagine, the aircraft grade ain't particularily cheap, so it's advisable to obtain it as scap from a shop that specializes on airframe repairs.