Tried downloading an ebook through the Overdrive library lending interface onto a Kindle device, a service that became available about a month ago. Anticipating problems, I haven't been able to get to it till now. (If I'm trying something new that involves business, bureaucracy, or machinery, or especially any combination thereof, I assume a five-minute chore will take an entire afternoon. Cynical as this view is, it has often proven accurate.)
I accessed Overdrive via a desktop computer and put the book on a free Kindle app on an iPhone. The process is twofold, requiring signing in to Overdrive to choose the book and then signing in to Amazon to send the book to a Kindle device.
The whole process went surprisingly smoothly. At first it didn't look like it had worked, but I found the book under the app's "archived" items and from there loaded it onto the main list of the app's home page.
This solves the problem of Overdrive's refusal to support 3G versions of the iPhone operating system, as the books actually come from Amazon. Now they just need to vastly increase the range and number of available titles.