Here's a golden tip since you live nearby, I assume you will stop in Punta Arenas, Chile. Take the slow boat trip to Isla Magdalena, and you will be walking in the middle of lots of Magellan penquins. Don't tell any one.
In 2016 I lost a suitcase after a tight connection in Amsterdam to Barcelona, I tracked it all night and saw that it arrived in Barca, but where? When I boarded the Prinsendam the suitcase was sitting in my room, that was the old Hal way.
Did you check with Lufthansa if you can make the connection in Frankfurt easily? Normally it will take about 45 minutes to get your luggage transferred from the Amsterdam- Frankfurt flight and FRA doesn't have the same problems as AMS airport.