It sounds like ATC (causing the plane to not reach its "final resting place" for a while) and the ground contract support were the issues. The original COR gate probably filled up. It also sounds like LATAM didn't operate at 100%.

Curious if during this very tight connection if your baggage made it?

Look, I understand, I've been there. At least you were @ SCL transit security and not LIM, where you've got the same tight connection and have a full transit security hall.