Aha! Figured it out.
The shop couldn't figure the problem out because it just wasn't making the noise for them. I picked up my car yesterday because I have to get to work somehow, and when I cranked the heat, the sound started immediately but only lasted for about 5 seconds, then went away again.
Later, while exiting the highway, it started really loud again, so I turned off the blower fan and it stopped right away. Finally, a diagnosis.
At least I know that my car won't explode now.
I do need my heat however as it is about -10*C (-28*F) every day now, so I still need to get the blower motor replaced.
Thanks for reading this post, and I hope it helps someone in the future.