> I am curious about the last assumption: Wood products can hang around for quite a while, so while long-term decomposition may release their carbon into the atmosphere, in the short term we have some very old wood around.

I have a hard time thinking of significant amounts of wood that doesn't decompose, unless treated by humans. There are exceptions, including petrified wood or maybe wood in oxygen-deprived water (I don't know much about that) but I doubt it adds up to much. I know I've read studies about the carbon released by decaying organic matter in rivers and river deltas; it's a well-studied process as far as I know.