Sorry for wasting forum space without being helpful...
But, this has been a growing problem since the reliable OFP game engine days.
The BIS games get better and better in terms of gameplay, but for us "cutscene directors" it's a nightmare.
The AI and environment is now more real and unpredictable, unfortunately you can't turn it OFF.
I wonder if the new "play video" function was implemented partly because of this issue.
Record your scene on video and make it the cutscene... No risk of rabbits messing up the cutscene.
In the good old OFP days the AI was stupid, but at least it did what it was told during cutscenes.