Lots of places in Canada are less than a day drive from the US border, might as well take a road trip and see what happens at the border before concluding anything.

Actually, if it were me I would pay the $50 CAD to apply for NEXUS. I have no idea if application for admission withdrawn is automatic disqualifying or not. If not then conditional approval at least lets you talk to a US CBP officer.

Even RT same day YYZ-JFK is cheap enough to try and with preclearance knowing if OK before even getting on the plane...