Update!
So after receiving a very confusing letter (see previous posts), I actually received my SIN on Thursday.
Timeline:
April 3rd - Passport with COPR, application, letter of urgency, and pre-paid express return shipping mailed via Canada Post
April 8th - Application received in NB
April 13th - confusing letter mailed by SIN office
April 21st - confusing letter received by yours truly
April 23rd - SIN received in the mail, along with passport
Unless you paid for express shipping, it most likely will take a while for them to receive your application. The postal service is very delayed at this point.
I hope this helps anyone waiting. And yes, they do hold on to your materials until they issue the SIN. It's very nerve-wracking.