I can only say that my experience says do nothing as with LAN there is the probability that the flight will either change back to the original time or they will make sure you make your connection. IME showing up at the airport with a printed, confirmed itinerary gives you more ammunition than trying to fix it on your own ahead of time which can cause more problems than you started with.
On the other hand, I agree that BA should be dealing with this. If you are not willing to let it ride, I would call back until you get an agent who is willing to do something proactive.