What Danish lacks is the “sing song” effect that Swedish and Norwegian both have; that’s probably why it sounds a bit different. It achieves the same effect as the “sing song” by using a kind of glottal stop. In written form, it is extremely close to the Bokmål variety of written Norwegian. That’s because Norway was effectively run by Denmark for many centuries (the history is somewhat complicated). (After Norway achieved full independence, there was a move to establish a more “Norwegian” writing system, and what resulted was something called “Nynorsk”. Both systems run in parallel, but I think Bokmål is dominant).
I went on a Danish kick after being inspired by “The Killing” and the other Danish (or Danish-Swedish) Scandi-noirs. However, the mismatch between writing and pronunciation drove me nuts. Eventually, I decided to concentrate on Norwegian. The grammar and vocabulary is very very close to Danish, and using Bokmål, in written form it’s hard to tell them apart. But the pronunciation is different, and there is a rich variety of dialects to add to the fun.
But I would say that Norwegian pronunciation is somewhat closer to the written form than Danish is.
(I suppose Danish would actually lend itself to the SSi approach, given that the latter does not depend on reading or writing).
This is a well-known Norwegian spoof on the Danish language: 