US CBP won't even know if you move your car as you won't be going to any US office on your way out.
I had moved to Canada for 13 months on Work Permit in 2015. I did thorough research back then. US had introduced this AES system and not many people ( even movers) knew how to work with it so I decided to skip "export from US" part as it was not mandatory for me. I directly went to Canada checkpost and "temporarily" imported my car into Canada. Registered my car in Canada and exchanged my DL.
In 2016, I moved back to USA. I showed up at US check post and told them that I moving my car from Canada to US. I was directed to secondary inspection/customs area ( things are hazy as its been 2 years). Their I showed my Original bill of sale ( from the time I purchased car in US) and received CBP 7501(?). Went to DMV, showed CBP 7501 and got my car registered in US.
By the way, keep a copy of title with you as in Canada you will surrender registration+title and will only get registration in return. Their is no concept of title in Canada ( as far as I know). This will help you if you decide to move back car to US. I had shown Original bill of sale but CBP prefers to see car title.
Tagging
@technokedar as he might be moving to Canada on work permit.