I appreciate the many replies and clarifications.
Addressing one of the comments above, yes, I absolutely plan on keeping my US citizenship. Perhaps it matters when I would attempt to bring in the firearm as in before I become a permanent resident (and hence am considered a tourist or visitor) or after I became a resident. Obviously I'll still need the license, training course, application, etc but I'm wondering if those suffice to sort of let you keep any (non restricted) firearms you brought in from America while you were a visitor.
For example. .. say I'm on a standard visit stay here (which is accurate) from a legal status standpoint. I go through the firearms licensing process, get the PAL, but before I become a permanent resident (assuming Ottawa approves me and this will take a year or more in all likelihood), I cross the border legally (declaring i have a firearm and showing all paperwork and licensure to CBSA) and attempt to bring in this firearm I bought in the US. Essentially I'm wondering if anything changes regarding the legality of my non restricted firearms that I bought over legally as a tourist the minute I become a permanent resident.
And I will as suggested above be looking at sources of information from the states on this topic. If anyone had experience with this then your thoughts would be appreciated.