Well, I'm back and I have to say the transit at AMS was simple and stress-free and my baggage made it as well. Guess I was being paranoid about nothing.
This was also the first time I've travelled buisness class (KLM) and it made a long flight (To Lima) a pleasant experience. It was a lot more expensive though, I'll have to ponder whether it was actually worth it just for continous free drinks and a lay-flat seat. On balance, on long-haul, I think it probably was.