They got the wood just as they got all the food and water they needed. The zealots had wood too, to build the inner wall. Wood is not the issue here. Remember, this is Rome we are talking about... many things are possible.
They already destroyed the stone wall, all that was left was the wood wall that couldn't be rammed down.
Like Kosmo said, you can't deny your only source. A lot of content is questionable, but most of the figurative language has already been picked apart. Archeology is our best friend.
Buy this and watch it: History Channel
You need more details on how they handle Josephus. Check archeological books/articles, for some evidence supports his work while some does not. This topic truly is a mess.
http://www.unrv.com/forum/index.php?showtopic=4469
I am currently working on a documentary about this very topic! Check it out.