While I dont have an answer, I face a very similar problem.
I moved to Canada recently and hold a EASA PPL/IR/MEP license (500+ hrs). Also I have a FAA (based on) license. I would love to obtain the Canadian license and am not sure about the TC regulations and have (so far) no found anyone knowledgable about this topic. What is the best way forward?
Alternatively I am thinking about buying/operating a N-reg plane on my FAA license, so I would also be very grateful about information about this way forward.
Thanks!