Attack the press and be aggressive. Don't settle for just getting the ball across half court. The key is the first pass should not go to the point guard, but the 2nd pass vs the press should. After the initial trap, your primary ballhandler will have the ball and start the run out on the break.
While I generally agree with your post, the key to breaking the press is keeping the ball in the middle of the court. Out of the first trap, you can reverse the ball back to the middle of the court and then attack upcourt or attack the opposite side. Alabama has enough decent ball handlers that the PG shouldn't be the "only" option in breaking the press. Of course, this will depend on preparation and strategy.