I dont know what to say about the immigration thing, but I can tell you about what I did in converting my Canadian ppl.
I did my private pilots license in Canada and then moved down to FL to continue my training. This was back in 2000, so Im not sure how things have changed, especially since 2001. I had to goto the local FAA office and show proof of my canadian license, medical and FAA medical. They then gave me an FAA ppl with the same restrictions and limitations that my Canadian one had (since I didnt have a Canadian night rating, I couldnt fly as PIC at night in the US). However after I got my Commercial pilots license, it superseded my Canadian ppl, so I no longer had that limitation. Again this was almost 8 years ago, so Im not sure if things are still the same.
Hope this helps!
BTW how hard is it to go from FAA to Canadian license? I earned my Canadian ppl but havent had a review or additional Canadian ratings since 00. Would be nice to be able to fly when I go back to visit. Thx!