I think it's 5 segments OR 10,000 miles - either works. The OP should have realized this and flown 5 times from YVR to ORD on AC to catch his flight to WI. As with speeding tickets, ignorance of the law is not a defense...
That being said, it's probably dumb of AC NOT to offer a soft landing to someone - hell, even US offered me a soft landing when I switched my flying.