Got travel insurance!
Took some time today to look into the different options I have for travel insurance. The danish national health insurance only covers me within Europe and my regular insurance covers travel for up to one month, so I needed something else for the rest. I ended up buying an insurance from Gouda, which should cover everything for the entire trip, including theft, baggage, medicine, transportation and so on. Most importantly, it fully covers in case of injuries or accidents from all sort of sports (only exception is skiing), so that was the selling point for me. Ended up paying 3377 DKR for the insurance, which is equivalent to about US$620.
Ready to go!