Thanks for the input! The letter of intent is interesting. I'll read up on it. Glad to know it seems like I have options, though!I don't see how this will be an issue. There are inland people in Quebec who just gets landed virtually (they do have to provide a letter stating they do not intend to stay in Quebec after being PR though).
@cemivac I'm sure if you are already in Quebec, you can be landed as inland. Once you are in, update IRCC with your new address and an LOE stating your temporary purpose in Quebec and make it clear you not intend to stay there past your internship.