Late response, but this is for anyone else if they happen to find this.
I'm aware that it is possible for an output to be triggered every time a team wins (tf_gamerules, OnWonByTeam1/2), but I'm not sure about it when it reaches 0.
As for the point owner reset, the koth logic entity creates two entities named zz_red_koth_timer and zz_blue_koth_timer, both for red and blue teams respectfully. These both have pause and resume inputs that allow for either timer to be paused and resumed at will.
Perhaps you could make it so that when a team captures it, the timer for that team is resumed, but when it sets to neutral, you could send the pause input to both. You'd also need to send inputs to the model and control point to set their owner to Team 0 (Neutral), amongst other things.