I think a lot of people are forgetting you can plant trees on your island... just get 4 jungle/spruce/dark oak sapplings, put them together and bone meal them, or even better use enchanted bonemeal you can buy at the farming npc for like 100 coins, insta grows anything. No need to compete for wood
One thing to mention : In some cases, you might have more speed using 3/4 Young and Rancher boots instead of full Young Drag. (It might be unnecessary and sorry if I missed it in the video lol)