So, this is what I did finally.
I returned to my last save game and began the invasion of Portugal again but now with the limited aim of making her a Puppet state of mine. Once I did that I went in the best of EU2 spirit and loaded a expeditionary "army" of three divisions unto my "fleet" and took them to reclaim the new world.
I took out Venezuela (LOL) and in quick succesion, Colombia, Ecuador and Perú.
Now I´m a Oil rich bastard with the huge producing Maracaibo Province and I´m only missing the Rubber which I´m seeing gets produced in Brazil...

...I´m not there YET.
The AI is terrible and my walkthrough South America with those same three divisions is a joke but I´m having my EU2 flashback
So, now all its about setting up those convoys (odd enough I´m getting more and more shipping although I have not ordered a single boat to be launched).
With oil, steel and coal my economy is ready to go and working 24-7 only with some problems when the rubber imports through trade get few.
I do have noticed that my production falls dramatically when I´m at war for longer then two months. How can Germany cope with this in a year long war?