Another note in favor of the "conditioning is relative" idea: The Ironman Triathlon. I vaguely remember a story about a runner who decided to enter the Ironman, and his observation that bicycling was a different set of motions from running. As I recall, his first few months of working up bicycling were months of "I thought I was in condition," aspirin, and collapsing after cool-down.

I'd suggest that you add running to your exercise, but only once or twice a week. Of course, this is coming from a person who is perpetually out of shape, so what do I know?