If you recall, they told me it would take one to six months to hear back.
Turns out, they miscalculated. I received my Danish residency letter yesterday.
That letter (which was written in Danish, so I had to type the whole thing into Google Translate to know what it said) says that I am now a legal resident for the next five years, with the option to apply for permanent residence some time before that five years is up.
That letter also allowed me to walk into the Kommune office to get my CPR number. And now that I have that number, all kinds of doors are open to me. I was given a doctor on the spot, so I now have medical coverage. I was able to go into a bank and open an account. And I was also able to get myself a phone with a local plan.
Most importantly, though, I can now register for Danish classes and hopefully start full-time this fall.
Looking forward to bidding a less-than-fond farewell to my regional illiteracy.