If you want to go all in on modular, wood based, zero carbon housing then learn how to build a timber frame house. If you really want zero carbon you can use only hand tools and harvest your own trees.
Wikihouse seems more for people who want to buy something off the shelf, pretty much a kit house. That's not a bad thing since it takes a lot of effort to build something as big as a house and lots of people don't want to do that. But I don't think this should be sold as a solution for DIYers since the existing methods already satisfy the listed requirements.