Do you need to track straight ahead till 3000ft or are ATC responsible for ensuring your new departure will keep you safe.
You have done your pre-flight planning well, now take that to the next step. That is, I would encourage you to clarify this before takeoff.
My opinion is that I am always responsible for my own terrain separation. For South America flying (and any flying in mountainous terrain areas), I suggest this is procedure, not technique.
What part of the world is this operation takeing place?