Since people kept insisting that it's correct to call obama "president obama", because Presidents don't lose their titles, he should have gone straight with "Office of the President"
It's not the "Executive Office of the President of the United States", so, they can't complain about that either.

We'd have the "Office of the President" in the Winter White House.

He should absolutely always refer to Mar-A-Lago as the Winter White House, since it's an actual name it always had.