Alternatively, we give the owner of the thread a bump button which they can do at any point allowing them to bump their threads strategically or when they are online. Don't allow posts to bump threads anymore. Only allow the button to appear every 24 hours.
What about bumping the thread only when OP posts a reply and his reply should receive at least one merit (the next reply should be merited by another user to bump the thread again).
This way we ensure OP is active and interacts with other users.