Well, I wouldn´t try to implement the original K2 livesearch, and search for another solution, e.g. this one at orderedlist.com. Why? Because the K2 one needs many changes – in my opinion to many changes.
Another Option: The old K2 livesearch used in the early K2 releases.
And another thing: It would be nice to have (if you have bbPress integrated with WP) one search to search all…