Before cancelling the press briefings, President Trump should try cancelling the tweets.
But as Suppressed suggests, let's not get all hung up on the impossible.
Perhaps the solution is to make clear that the press briefings are limited to actions taken by the Administration, not Trump's tweets. That is, make clear that the tweets represent personal thoughts of the man, and not statements of the President with any official ramifications. Let Trump and Trump alone answer for his tweets, not his press secretary.