The answer is ... It depends. There are several features to a press defense: one feature of a press defense is that teams running it tend to commit more fouls. Post players with good lp and solid ath draw fouls. You have multiple post guys with solid to good lp and Ath.
One thing that is part of coaching is that several contradictory principles on what to do in a generic situation can all be true depending on the specifics of the game, you can say "generally feed the ball to your high bh/high pass guards and players" and that is true. But you can also say "feed the ball to your best players because they can't double team or play a matchup game on you" and have that be true. Or "feed the ball to your post players that pick up lots of free throws and collect fouls against the press' and have THAT be true. It's a game of balancing the competing truisms and principles based on e individual game, where your strengths are and where their weaknesses are. You are trying to maximize and capitalize on your strengths, minimize and work around their strengths, exploit their weaknesses and hide your own. And the means of doing that are not always going to be the same from game to game depending on your opponent.