not sure if it’s appropriate to mention here but I’d be willing to pay a developer decently to come up with this extension (with at least with basic functionality such as auto-approve after 5 posts). this would cut down my time to moderate and time is money, as they say.
There is add-on by silenz Moderate Once which has very similar functionality for comments. According to its docs:
With Moderate Once only the first comment of a person needs to be approved. Once that first comment has been approved any subsequent comments by that person are no longer moderated and get posted automatically.
Perhaps this free add-on could be hacked to provide functionality you need for forums.