I would like to summarize the ideas that I have learnt from the other answers into an effcient, potent compound.
Appointing active maintainers
The key seems to be assigning "owners" (active maintainers with elevated authoring privileges) to different subsections. Specific departments could appoint their own elevated maintainers.
- Owners could merge duplicated pages within the scope of their own departments; perhaps while keeping in touch with the original authors of those pages.
- Cleaning up / managing keywords and keyword aliases could also be their task.
- Owners could scan for outdated content and either update them themselves, or could delegate the updating to peers in the same department.
- Optimally, it should be peers who self-initiate the content-updates. The owner is just an extra pair of eyes who, after familiarizing themselves with the volume of information, would develop a sense (or methods) for pointing out potentially neglected parts.
- Keeping up order and preventing relapsing into chaos again seems to necessitate that non-owners have less-than-ultimate privileges.
- While managing content within pages would be everyones privilege, renaming, merging, deleting (and in a daring experiment, possibly even creating?) pages could be tied to an approval or to following suggestions from the assigned maintainers.
Reining in redundancy
In summary, the aim here is not "eliminating" redundancy. This suggestion is about replacing a worse kind of redundancy with a more manageable one.
Departments seem to organize their subsections primarily to be consumed internally. Now, for something new, departments should establish a new document format: a simplified, shortened, tasks-oriented variant (of select existing documents) that is aimed at users working in other departments.
This would allow info to remain in the scope of the responsible department. When a product gets an update, then the corresponding owner would know to update both the canonical and the simplified document variants with the new info.
These guest-oriented documents would rely on suggestions from "guest users" from other departments: they should communicate their needs and suggest the content that should be included for them. The owner from the host-department could approve / implement these suggestions, and later both ensure that all "guest personas" remain supported by the content, and update information within whenever the subject of the documentation itself changes.
First of all, content-maintainers from all departments should come together to study and (hopefully) agree on organization patterns that they would subsequently follow in their subsections as best as they can, allowing the entire wiki to uphold consistent organization patterns — a pillar of usability.
Regarding the sections that involve several departments: these could be sorted out by letting the corresponding owners actively organize the work among themselves, first agreeing on who's responsible for what parts exactly.
The initial part of the tidy-up:
- the familiarization with the contents,
- identifying patterns,
- coming up with reorganization opportunities and verifying them with involved peers, and
- implementing the reorganization
could demand a dramatic level of involvement from the appointed maintainers. In this short initial period their workload would need a bold adjustment to accommodate this intense effort.
Regular maintenance activities also demand sustained efforts, only on a significantly smaller scale. The need to allocate suitable time for the tasks remains necessary.
It's worth reiterating that the overall efficiency of maintaining the wiki will rely on the contribution of all team-members: while maintainers should serve by sort of directing the traffic, the heavy lifting should still be done by normal users contributing the mass of the content.
People losing their current bookmarks and suddenly getting lost in the reorganized system can be modeled as a persona whose needs need to be addressed.
- The tidy-up operation and its expected benefits need to be communicated company-wide.
- There could be a new page established with the organization chart of the newly appointed subsection owners, so in the first weeks of the re-adjustment phase, hopelessly lost people would know who to turn to for assistance.
- Perhaps, instead of relying on page redirects, old pages (whose content got merged into other prevailing documents) could be kept, but their content could be reduced to just a message about the migration of the information and the link to the new location. This would allow people to get a better grip on the situation and update their (mental and actual) bookmarks. These old pages could also be stripped of their assigned keywords and perhaps other metadata, so that they stop polluting search results.
- People should be taught that in the new system they can rely on the content owners' collaboration and it's not necessary any more to keep their own redundant copies of information.
- They may choose to maintain their own personal copies, notes, bookmarks, but now they will know where to look when their unofficial copies get out of sync.