As you figured out, there is no way to 'animate' your tiled background.
(Just save the picture, it's too big..)
Because I can't post links on the forum, I have screenshotted how I fixed the problem.Basically was happens is when woodFloor1 it's pivot point hits 0x, it spawns back to 640x (Just multiply the screen width.)
With a bullet behavoir it looks like it's moving, and because the same tiled background (woodFloor2) follows, it looks like it's being animated.
There is a lot of room for improvement though with this kind of method. For some reason I got sometimes some white gaps between the two. (Maybe add a third backgound, or put the tiled background closer together.
Hope this helps!