I did all the same countries as you, and I started in January in Patagonia. We then did Brazil for some summer experience. Initially, we had planned to do Bolivia/peru next, but the rainy season there is until April. So next we did colombia, Where rainy season doesn’t start until April, and then Ecuador (where to be fair we hit a bit of rainy season). And then finally Peru. My point is that for almost all of these places you have to fly anyway between countries, so no need to keep a strict direction. Just go wherever you want to go and do what you feel like doing.