You will have a marvelous trip! I concur, don't be a slave to your equipment. Remember the weight and bulk of what you carry. I am almost your age and don't want to carry too much, especially if it is hot or I am at altitude. I have traveled extensively with what I call my "Travel Triumvirate"......the 24-105+70-200 f/4IS and 17-40. Before I had my 5diii, I carried the 15-85+10-22+70-200 f/4IS with my 50D. That is it.......no tripod or super-white or flash or anything, just those 3 items (unless it is a photography trip like to Bosque del Apache). If I am trekking, I use a backpack (F-Stop Loka). If I am walking around, I use a messenger type bag (Thinktank Retrospective 7). I might not get photos that warrant hanging in a museum, but I get quite a few keepers that work for my purposes. You can do a lot with some cropping and post processing that will make up for leaving your 2.8 at home.....Look at:http://jpacker.smugmug.com/India-2014/Madurai/
to see what I have done with all existing light even in the evenings. And your 6D does really well at high ISO settings.
As far as security is concerned, just be smart. I agree that I would not call attention to yourself with a "front pack." Besides, that is not an ergonomic way to carry a load. There will be a gazillion folks at Machu Pichu. Be sure to get the sunrise shot and the overview shot. Please let us know about Easter Island. I'd love to go there some day.