Have these briefings by fax. Send it to one machine in the basement of the White House. Make the ridiculous press corps take numbers like at the deli. Then escort them in AND out under armed guard one at a time.
See how they like that.
L
Have them email or tweet their questions. Any the President feels like answering gets posted to the White House web site.
There is nothing in the Constitution which requires the President to talk to reporters.
Who on earth uses a Fax these days?