Thanks guys. I called again yesterday and spoke to a different agent. I was quoted just under 700dkr for the EB ticket. So the first agent was clearly lost when he gave me that crazy price.

Regarding the Swiss alternative with EB points, yesterday I was quoted 3400dkr in taxes for a ticket that costs 4500dkr in cash.

So it seems like I'll just buy the tickets instead. I enjoy flying Swiss and the flight times and connections are just better.