Actually multiple persons in my idea were added just for the sake of redundancy, namely to avoid that the disappearance of someone involved would stop the process as a whole. The system in my opinion will then always work if the minimum number of actors is present.
You pretty much nailed how it's done, good show for off the cuff. Encrypt file with large symmetric key. Slice into n pieces, where n is like 5-10 or more. Distribute a few copies of each slice to reliable people unlikely to directly conspire. Distribute encrypted file widely. Give instructions on how to gather as a group based on some basic trigger. The chance of the gathered group missing every copy of one of the slices is pretty low as long as nobody gets a master list of key holders.
