We could try to develop a new extension or improve on an existing extension for our forum, but that seems like a lot of unnecessary effort, especially when there are perfectly good standalone forum packages available. But, a separate forum package requires a separate user account, and we would not want for people to have to log in twice to do whatever. So, assuming we go with a standalone forum, we would need to develop an extension that would integrate user authentication between the wiki and the forum.
There are a couple forum-integration extensions out there, such as one for phpBB. However, these extensions don't appear to still be maintained and have issues of various degrees. The phpBB extension works, at a basic level, but it doesn't handle internal capitals and special characters well at all— though it could still be used as a basis for whatever extension we go with.