While the press could be stopped from distributing videos and pictures I don't know about FB and other social media. Texting can spread like wildfire as well. Hey Joey watch this and Joey sends it to 10 friends who send to to ten friends etc.
My thought would be to shut down the video as much as possible and especially publicly but immediately allow high profile, in this case BLM, leaders see it. The family too but warn them it is ugly. Explain that a release of the video could jeopardize a conviction on a juror selection basis. Let the concerned parties know the prosecutor's intentions and keep them advised of progress.
Ask the leaders to advise their followers that they have seen the videos and have agreed that justice will be better served by keeping it confidential until the trial is over.
Does the family want to see the video replayed every time the media has a slow day and finds an excuse to replay?
I hear a lot of "The public has the right to know" talk. Do they?
Isn't it more like "The press needs something to sell papers or score viewers".