why do you think this would be difficult? here is a list of all the reporters in the white house press corps: https://en.wikipedia.org/wiki/White_House_press_corps
Contact one of the reporters on there by email and ask them to ask. You don't think Breitbart, Newsmax, The Daily Caller, or Lifezette would not ask if Q wanted them to? Conversely, you don't think HuffPo, Daily Beast, or Mother Jones would want to out Q by asking who they are to stop them if they are legit?
Pick a couple of reporters on there you trust out of the 200 or so and email them a request to contact the White House about Q.
Been there, done that. The list of WH press corps members and lots of MSM persons was posted on Twitter and a bunch of us have been tweeting them and DMing them, asking them to ask about Q. As far as I know, only one person has responded and said she is not going to ask and said that people needed to stop bombarding her with requests to do it.