Alrightty, I got it figured out (and got my gun!).

Before going to pick up, I had to have:
(1) Buyers transfer form (received from RCMP in the mail)
(2) Registration (received from RCMP in the mail)

Then the seller receives:
(1) Seller transfer form (from the RCMP)

THEN, I apply for and receive:
(1) STATT (short-term authorization to transport).

After killing those rainforests, I was able to pick up the new firearm.

Looking forward to hitting the range tomorrow (yes, I have my LTATT already)!