Yup, soak up the experience and figure out a design that engages that experience. This applies to software design as well. In my experience, this is really how good software design gets done; all the fancy high falutin' processes result in boring, bland software.
Several years ago, I figured out that a significant part of a designer's job was to (somehow) come up with the correct solution for a given problem and then sell that decision to the client. For me, like Jeff, the solution would usually arrive fairly late in the game after I'd been soaking in the problem for 90% of the available time.