Bay,
I imported a project from the UK to the US some years ago. The rules for projects are the same as for completed aircraft. Here's my understanding.
Only US citizens, permanent residents or US based companies can own aircraft on the US register. I deregistered the aircraft from the UK CAA register, but since I came to the US on an H1B I was then unable to register it with the FAA. This was a probem, because I couldn't get insurance for the project without an N-number. Fortunately my wife is a US citizen, so I sold it to her, and it's now registered in her name.
I understand that the rules are the same in Canada, and heard from an expat over there that the option of registering the aircraft in the name of a shell company and leasing it back to the temporary resident is realtively easy and legal.
Costs are minimal, and I got a lot of help, advice and clarification from the FAA representatives at Sun-n-Fun some years ago.
Regards,