We have some progress!
A few days ago, I wrote back to the immigration people asking what had happened to my case. My previous theory that observer effect could be acting on the process may be true after all. A couple of days later, I got an email with this in it:
Our system indicates that your USCIS Immigrant Fee was received on February 10, 2015. Your Permanent Resident Card is currently in production. You should receive your card within 15 business days. If you do not receive your card within 15 business days of the date of this notice, please submit a follow-up inquiry
Not only had my status been updated on the immigration site, I could also log in to another part of the site to see this:
Here’s the video: