Hi
Registering a car in Indiana can be done with three pieces of identification: a passport, a social security card, and proof of residence such as a rent receipt, telephone bill, etc. I have all three. Producing an Indiana driver's license is not a requirement.
It sounds from you post, though, that the driver's license is the key document that would end the argument over car registration. Do you think CBSA would deny me and my car entry into Canada, or require me to remove the car from the country after a specified period?
They would allow you to drive the car from the Port of Entry to residence, and then from the residence to the US when you leave. That would be it.
PMM