1.4.4.9, glitches, not seeded.
Uses some glitch with the achievements menu that lets you take items from the crafting list, which in this case is the zenith. This run is better than my first one posted, I refined my strategy a bit. This time, I used the worldgen preview mod to cherry pick good spawns (lots of trees near spawn, no tall trees) and ONLY looked for the wood drop when shaking trees.
Again credits to eatpotaro for the idea.