I still think the only practical Starships that could be used as a "Presidential ship" (other than whatever ship he boards in) would be a Galaxy-class starship or similar-to but not really one, like maybe an Intrepid or Cheyenne class if something smaller is needed and not a Galaxy or Nebula-class (one modified for luxury). But I believe a Galaxy-class is better than a Sovereign or a ship in Q's alterbate reality such as the Olympic. A Galaxy-class is most symbolic for a Federation President's needs from the 2360s to whenever it retires.
However, that design is nice for a 25th-century Federation Starship based on the Galaxy-class.