I ran into a similar (but not exactly the same) position years ago, but everything I have done wasn't successful. So my points may not worth much.
From what I have known:
- A forum almost always has greater influence than a wiki of the similar size to average users participated in both, and encourages contributions more. (A StackExchange-like model lies between them, and there is nothing else between the three.)
- Forums are much harder to maintain than a wiki, when there are too many users (1,000,000 or even 10,000,000 users, say). That might be a big number. But for a single user, it is still easier to join many wikis with a total of 1,000,000 users, than many forums with that many users. That's how a wiki can be successful.
For your question, there are two obvious (and conflicting) ways based on these assumptions:
- Try to attract some users outside your forum, and try to make your wiki not very forum-centric. It's fine that your wiki has less quality, and only a few users are active and volunteers to move the conclusions from the forum to the wiki (at least they save time for reading the whole thread; but users already always reading whole threads may not be interested). And of course, don't require moderator approval to edit. Wikis need less moderation but they still need some, and there are also spambots on forums. You could also try some automatic filters, or setting minimum time to wait before first edit after registration.
- Or try to make the wiki something inside your forum. At least wiki edits should be scored, being indistinguishable with a forum post. And other users can reply to or argue with those edits, and also scored, in the same way like the forum. This may nullify everything good for a wiki, and stop attracting more users than the forum. For example, some may say the current revision is far from the conclusion, but based on personal opinions, and don't want others to remove it without good reasons (much better than nobody ever tries to write something in the perspective of forums). But it's fine if you don't have those 1,000,000 users, and you just want to use the wiki as a tool.
- But well, we didn't have enough programmers for that non-profit wiki to make them real.
- An easier way is to link the announcements to the wiki, and link from the wiki back to the original posts. It may make users complain less but I'm not sure about anything else.
Another option which seemed not to be what you want: Chatrooms seemed to be more compatible with a wiki than a forum because they don't share functionalities. I don't see a feasible way converting a forum to be like a chatroom. But one way is to let the forum users also join some chatrooms they like, and introduce the wiki to some chatroom users who aren't really interested in forums. Though it may be not easy to do it right.
Restricting the forum to talk about topics on the wiki may also work, but that's stupid since you had a successful forum but not a successful wiki.
TL;DR: Who will decide who is right and who is wrong when two users don't agree with a wiki edit? Think of that. If you don't like those arguments, you have to move them elsewhere, or move to some earlier time.
Wikis aren't automatically having a higher quality. Either improve that or let your users know. When users are saying "wiki is good", they are in fact referring to some unknown wiki editors being good, which probably means they are not editors either. If there are someone don't agree anyway, it's reasonable to think arguing with someone known and being serious better.
Instead, if they are changing the wiki after those arguments ended, they are on the right way.