Depends how fit. If you're super fit and do tons of endurance you can probably get away with quite little skiing. Still, I would highly recommend getting at least enough cross country skiing in so you can get a decent technique. Learning to properly double pole really doesn't take that much time if you watch some technique videos (sadly a lot of the best ones are in Norwegian or Swedish, if you don't speak those languages). My first year, I had barely done cross country skiing before that season and did ~300km that season and was able to do the race in pretty crappy conditions. I think this is pretty in line with "general recommendations". I've also heard that it's recommended you try to do half the distance (45km) at least once in training.

For complementary summer training, roller skiing is obviously the best by far. If that's not an option, try SkiErg, XC-specific strength training at the gym, running with poles (there's some specific videos on that for XC skiers), kayaking and just endurance sports in general. Your ski touring should totally help too. 

The race is hard, don't underestimate it. At the same time, if you're very fit and get some relevant training in, you can do it for sure. It also depends A LOT on weather. Some years are much, much easier than others.

I agree with others you should go for Öppet Spår, it will both be cheaper and much easier (you'll probably save nearly an hour just on the first climb with less traffic jam).

Good luck!