TinyMCE has a [url=http://www.tinymce.com/tryit/3_x/bbcode.php]BBCode plugin for forums[/url] available. Hell, it's already right there in the TinyMCE bundle that comes with SS framework. (\framework\thirdparty\tinymce\plugins\bbcode)
So, uh, why isn't it being used?
Granted, the plugin is based on punBB's dialect of BBCode, while IIRC SS uses whatever was on PEAR at the time (looked at any [url=https://packagist.org/search/?q=bbcode]alternatives[/url]?). So some tweaking would probably be needed, but the plugin is little more than a set of regexps, so I doubt it would take too much.
So what would be involved in this? Obviously you'd need a custom HTMLEditorConfig, and the post form would have to be changed to HTMLEditorField. But the actual data fields in the Forum module wouldn't need to change since it's still unparsed BBCode being sent from the user, right?