Thanks for the input guys. Much appreciated.

I'll call them again tomorrow to find out the breakdown of the taxes they want to charge.

For what it's worth, in one of the alternative routings I checked flying Swiss, I was given a price of over 10.000 Euros if I was to buy a second ticket with money. Did I mention this was all in economy? A quick search on the Swiss site found those flights for about 5.000 dkr.

So I guess we can conclude the SAS system might not be very reliable.