The koth timer is started by an output on the control point's trigger_capture_area, right? Just add some extra logic to start the timer whenever you want it to, and add multiple control points.
If you want the timer to stop under certain conditions, you're going to have to directly stop the round timers created by the tf_logic_koth entity on map start. They're regular team_round_timer entities with the targetnames zz_red_koth_timer and zz_blue_koth_timer.