"The Physics Problem"

I think you're going to get a lot of error in your calculation due to the leaning tire and how its grip of the road will change. With the bike and rider you've got ~700 lbs of force (guessing) on a ~40 PSI tire and a footprint of (700/40) 17.5 square inches. But because you're sitting more on the sidewall of the spinning tire that rubber footprint is moving at different speeds across its width and gripping the road much differently than if the bike was upright.