US Certificate holders can obtain a temporary Equivalency License so that they can operate a Canadian registered aircraft. This used to be done in person, but with Covid, I did the whole thing via email. I was issued a six month license for "ferry and local flying" which allowed me to fly the plane across the border and then locally for a couple of days to allow M'lady to bend it around the sky a bit from the back seat. I did confirm with my insurance broker that I was covered under my current policy for such things.
Then the plane was grounded, and I sent the registration back to the prior owner for submission to Transport Canada for deregistration. Follow up on that process early and often, via phone call to Transport Canada.
I employed DixieAire in Oklahoma City at the suggestion of my DAR to register in the US. They were the ones who said it seemed there was a delay by Transport Canada, and once I was able to push the deregistration along, I had a temporary registration 48 hours later. Money well spent.
While waiting for registration, I performed an owner assisted condition inspection. After confirming a temporary registration was sufficient to move forward, I was able to schedule the DAR two weeks later. I made sure all the forms he wanted were available, and handed over several AMU's and listened to his stories. He sort of looked at the airplane. Again, money well spent.
My "American" plane was up and flying again after the grounding in about 30 days time.