I like to use the strangler fig pattern. This concept is used to build a new version of a system alongside an existing legacy system, but I think the idea also works for building a new documentation system alongside a heap of old unorganized info.
Start by building a structure with some empty templates, a d a few instructional examples. Then ask the team to bring over information into the new system whenever they find something useful in the old system. Minimally, ask them to drop a link in a relevant hub or two. Even better if they spend 5 minutes copying it over to the new system, and adding a note with a link to the new version in the old system.
Over time the new documentation system will strangle the old one. Hence the name.
Team participation is a must. This will not work if it is a one man effort. Have managers push and encourage people to participate in the documentation effort.
Side note: the strangler gig is a fazcinating plant.
