One option is to apply for Global Entry/NEXUS for Canada. You will have a single potentially miserable interview with a CBP officer who might bring your denial

One option is to apply for Global Entry/NEXUS for Canada. You will have a single potentially miserable interview with a CBP officer who might bring your denial up because I'm sure they ask if you've been refused entry before. But if they're happy, you can enter the border without speaking to any agents (or a significantly reduced chance). Once cleared, on arrival, they snap a picture of your face at a kiosk and wave you through on an iPad (no passport involved). It works out to around 20 dollars a year plus your home country's admin fee. This doesn't solve your problem entirely but if you're legally allowed to be in the US then there's nothing underhand about taking advantage of the program. I think NEXUS might be easier, but when I did this as a European the border agent didn't really know what to do and was very grumpy that I didn't provide a US address to send my card which I was told by a different airport I didn't need. Once that was sorted, I haven't had any trouble since and it usually eliminates queueing at the border. If you're physically in the US, do it at an airport if you can get an appointment - they tend to be much more relaxed than the border guards.