Well - Im not an South-America expert, have only been here 4 months as of now but I have been riding Europe to Australia and NZ so some experience from the road I have.

If youre planning 6 months for a trip like you mention you must race from place to place, country to country - well in my opinion then. What if youre bike break down and you have to wait 1-2-3 months for parts and repair? Half your time could be gone. South-America is a huge continent and so are north America. Chile and Argentina are both approx 5000 kms from north to south. The roads to the most extreme parts of this continent such as R40 in Argentina and the Carretera Austral in Chile are partly gravel - so not done in 100 km/h.
Of course people are different, some like to race from place to place and some like to stop and smell the flowers along the roads. But anyhow - 6 months seems to little for such a trip in my opinion.
Paperwise its probably the easiest continents to travel in. No Carnet required in contries, visas on arrival in almost every country. Insurance required but seldom asked for and reltively easily available and cheap.

You must contact a shipping agent for shipping prices but I would guess somewhere between 1000 and 1500 € for one way shipping Europe to Buenos Aires or Montevideo. And remember you might have to ship it home again. And currently there isnt any ferry between Panama and Colombia so you will need to fly it or find another solution there and it will cost some money.

Weather and climate wise for south-America I think its hard to tell an exact time that is best to go. The whole length of south-America are divided by the Andes mountains and that influence the weather and climate a lot. Most countries would have 2-3-4 different climate zones.
Theres one exception though and that is the far south part of Chile and Argentina called Patagonia. The window there is usually said to be between nov-dec to febr-march. But expect extreme winds, rain, snow and harsh conditions even in december and january. In Ushuaia it was fresh snow in the mountains down to 2-300 masl on christmas day last christmas.

And its very useful with some spanish skill too....

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In the end everything will be fine. If its not fine its not the end....