I think I'm finally figuring out what happened. I was walking around quite a bit in my mountain bike shoes, due to traffic conditions forcing me off the bike or because I reached a nice destination and just wanted to linger and walk around. The unfitness of those shoes for walking, combined with my foot's tendency to overpronate, put forces into the shin which caused shin splints.

Biking then exacerbated the condition, but didn't directly cause it. There's an underlying imbalance in my left leg and I have to straighten that out or compensate for that. I'm in the process of seeing a podiatrist and it looks like another round of physical therapy.

I use toe clips but don't really pull up on them -- I just use them to keep my foot in a reasonably good place. I'm torn about going to clipless -- presumably they give you the best mechanics; yet, I've several times been injured by apparatus that locks you into a position.