One way to do this, without causing too much confusion ("my cues not running" type complaints) would be to have a "Filter" toggle button at the top of the Active Cues panel. Then in the Basics tab of each cue an additional check box "show in filtered active cues list" which would be checked by default. When the filter button was pressed in the active cues list, only those cues which have the 'show filtered' check box checked (ie everyone by default, to not change current behaviour).
This would give users control over which cues are display in the filtered active cues list (could be whatever the operator thought was useful for monitoring, pausing/stopping or whatever) and wouldn't change current behaviour.
Paul